diff --git a/lib/package.gi b/lib/package.gi
index b6998c00f9..5ed19406dd 100644
--- a/lib/package.gi
+++ b/lib/package.gi
@@ -304,7 +304,7 @@ InstallGlobalFunction( InitializePackagesInfoRecords, function( arg )
     # the first time this is called, add the cmd line args to the list
     if IsEmpty(GAPInfo.PackageDirectories) then
         for pkgdirstrs in GAPInfo.CommandLineOptions.packagedirs do
-            pkgdirs:= List( SplitString( pkgdirstrs, ";" ), Directory );
+            pkgdirs:= List( List( SplitString( pkgdirstrs, ";" ), GAP_realpath ), Directory );
             for pkgdir in pkgdirs do
                 if not pkgdir in GAPInfo.PackageDirectories then
                     Add( GAPInfo.PackageDirectories, pkgdir );
@@ -1858,14 +1858,15 @@ InstallGlobalFunction( SetPackagePath, function( pkgname, pkgpath )
 InstallGlobalFunction( ExtendRootDirectories, function( rootpaths )
     local i;
 
+    rootpaths:= List( rootpaths, GAP_realpath );
+    # 'DirectoriesLibrary' concatenates root paths with directory names.
+    for i in [ 1 .. Length( rootpaths ) ] do
+      if not EndsWith( rootpaths[i], "/" ) then
+        rootpaths[i]:= Concatenation( rootpaths[i], "/" );
+      fi;
+    od;
     rootpaths:= Filtered( rootpaths, path -> not path in GAPInfo.RootPaths );
     if not IsEmpty( rootpaths ) then
-      # 'DirectoriesLibrary' concatenates root paths with directory names.
-      for i in [ 1 .. Length( rootpaths ) ] do
-        if not EndsWith( rootpaths[i], "/" ) then
-          rootpaths[i]:= Concatenation( rootpaths[i], "/" );
-        fi;
-      od;
       # Append the new root paths.
       GAPInfo.RootPaths:= Immutable( Concatenation( GAPInfo.RootPaths,
           rootpaths ) );
@@ -1889,11 +1890,12 @@ InstallGlobalFunction( ExtendPackageDirectories, function( paths_or_dirs )
     local p, changed;
     changed:= false;
     for p in paths_or_dirs do
-      if IsString( p ) then
-        p:= Directory( p );
-      elif not IsDirectory( p ) then
+      if IsDirectory( p ) then
+        p:= Filename( p, "" );
+      elif not IsString( p ) then
         Error("input must be a list of path strings or directory objects");
       fi;
+      p:= Directory( GAP_realpath( p ) );
       if not p in GAPInfo.PackageDirectories then
         Add( GAPInfo.PackageDirectories, p );
         changed:= true;
diff --git a/src/streams.c b/src/streams.c
index db5a23a2ac..48e2f5e8dc 100644
--- a/src/streams.c
+++ b/src/streams.c
@@ -1163,11 +1163,7 @@ static Obj FuncGAP_realpath(Obj self, Obj path)
     RequireStringRep(SELF_NAME, path);
     char resolved_path[GAP_PATH_MAX];
 
-#ifdef SYS_IS_MINGW
-    if (NULL == _fullpath(resolved_path, CONST_CSTR_STRING(path), sizeof(resolved_path))) {
-#else
-    if (NULL == realpath(CONST_CSTR_STRING(path), resolved_path)) {
-#endif
+    if (NULL == SyRealpath(CONST_CSTR_STRING(path), resolved_path)) {
         SySetErrorNo();
         return Fail;
     }
diff --git a/src/sysfiles.c b/src/sysfiles.c
index b4c0221de7..1187e4b0ff 100644
--- a/src/sysfiles.c
+++ b/src/sysfiles.c
@@ -2912,6 +2912,20 @@ Int SyIsExistingFile ( const Char * name )
     return res;
 }
 
+/****************************************************************************
+**
+*F  SyRealpath( <path>, <buf> ) . . . . . . . . . absolute canonical path
+*/
+Char * SyRealpath(const Char * path, Char * buf)
+{
+#ifdef SYS_IS_MINGW
+    return _fullpath(buf, path, GAP_PATH_MAX);
+#else
+    return realpath(path, buf);
+#endif
+}
+
+
 /****************************************************************************
 **
 *F  SyIsReadableFile( <name> )  . . . . . . . . . . . is file <name> readable
diff --git a/src/sysfiles.h b/src/sysfiles.h
index bca4cba689..3913a106da 100644
--- a/src/sysfiles.h
+++ b/src/sysfiles.h
@@ -350,6 +350,18 @@ void SySetErrorNo(void);
 Int SyIsExistingFile(const Char * name);
 
 
+/****************************************************************************
+**
+*F  SyRealpath( <path>, <buf> ) . . . . . . . . . absolute canonical path
+**
+**  'SyRealpath' stores the absolute path of <path> with all symlinks
+**  resolved in <buf>, which must have room for 'GAP_PATH_MAX' characters,
+**  and returns <buf>. On failure, e.g. if <path> does not exist, it returns
+**  NULL and sets 'errno'.
+*/
+Char * SyRealpath(const Char * path, Char * buf);
+
+
 /****************************************************************************
 **
 *F  SyIsReadableFile( <name> )  . . . . . . . . . . . is file <name> readable
diff --git a/src/sysroots.c b/src/sysroots.c
index 8b83b97902..39af197ab1 100644
--- a/src/sysroots.c
+++ b/src/sysroots.c
@@ -203,17 +203,27 @@ void SySetGapRootPath(const Char * string)
     // TODO; instead of iterating over all entries each time, just
     // do this for the new entries
     char * userhome = getenv("HOME");
-    if (!userhome || !*userhome)
-        return;
-    const UInt userhomelen = strlen(userhome);
+    if (userhome && *userhome) {
+        const UInt userhomelen = strlen(userhome);
+        for (i = 0; i < MAX_GAP_DIRS && SyGapRootPaths[i][0]; i++) {
+            const UInt pathlen = strlen(SyGapRootPaths[i]);
+            if (SyGapRootPaths[i][0] == '~' &&
+                userhomelen + pathlen < sizeof(SyGapRootPaths[i])) {
+                SyMemmove(SyGapRootPaths[i] + userhomelen,
+                          // don't copy the ~ but the trailing '\0'
+                          SyGapRootPaths[i] + 1, pathlen);
+                memcpy(SyGapRootPaths[i], userhome, userhomelen);
+            }
+        }
+    }
+
+    // make all paths absolute; paths that do not exist are left as is
     for (i = 0; i < MAX_GAP_DIRS && SyGapRootPaths[i][0]; i++) {
-        const UInt pathlen = strlen(SyGapRootPaths[i]);
-        if (SyGapRootPaths[i][0] == '~' &&
-            userhomelen + pathlen < sizeof(SyGapRootPaths[i])) {
-            SyMemmove(SyGapRootPaths[i] + userhomelen,
-                      // don't copy the ~ but the trailing '\0'
-                      SyGapRootPaths[i] + 1, pathlen);
-            memcpy(SyGapRootPaths[i], userhome, userhomelen);
+        char buf[GAP_PATH_MAX];
+        if (SyRealpath(SyGapRootPaths[i], buf)) {
+            strxcpy(SyGapRootPaths[i], buf, sizeof(SyGapRootPaths[i]));
+            if (SyGapRootPaths[i][strlen(SyGapRootPaths[i]) - 1] != '/')
+                strxcat(SyGapRootPaths[i], "/", sizeof(SyGapRootPaths[i]));
         }
     }
 }
diff --git a/src/sysroots.h b/src/sysroots.h
index 4b9dfde11f..ecf83d54c1 100644
--- a/src/sysroots.h
+++ b/src/sysroots.h
@@ -49,7 +49,7 @@ void SySetGapRootPath(const Char * string);
 **
 **  <buf> must point to a buffer of at least <size> characters. This function
 **  then searches for a readable file with the name <filename> in the system
-**  area. If sich a file is found then its absolute path is copied into
+**  area. If such a file is found then its absolute path is copied into
 **  <buf>, and <buf> is returned. If no file is found or if <buf> is not big
 **  enough, then <buf> is set to an empty string and NULL is returned.
 */
diff --git a/tst/testinstall/package.tst b/tst/testinstall/package.tst
index a2577c2519..10a1194161 100644
--- a/tst/testinstall/package.tst
+++ b/tst/testinstall/package.tst
@@ -690,6 +690,18 @@ gap> Last( GAPInfo.PackagesInfo.mockpkg ).InstallationPath =
 >      GAPInfo.PackagesLoaded.mockpkg[1];
 true
 
+# paths are made absolute, so equivalent paths are not added again
+gap> n:= Length( GAPInfo.PackageDirectories );;
+gap> ExtendPackageDirectories( [ Concatenation( Filename( mockpkgpath, "" ),
+>                                               "../mockpkg" ) ] );
+gap> Length( GAPInfo.PackageDirectories ) = n;
+true
+gap> n:= Length( GAPInfo.RootPaths );;
+gap> ExtendRootDirectories( List( Filtered( GAPInfo.RootPaths, IsDirectoryPath ),
+>        path -> Concatenation( path, "./" ) ) );
+gap> Length( GAPInfo.RootPaths ) = n;
+true
+
 #
 gap> SetPackagePath( "mockpkg", Filename( mockpkgpath, "" ) );
 gap> SetPackagePath( "mockpkg", "/some/other/directory" );