Designed for use in embedded devices the mGSTEP libraries implement a subset of NeXT's OPENSTEP specification which evolved into Apple's Cocoa frameworks. Applications can be built for either an X11 or Linux frame-buffer based GUI.
Development of mGSTEP has been intermittent for more than 10 years.
Better maintained options may exist (see below) and should be considered for all new projects.
mySTEP is a fork of mGSTEP that has been developed as a platform for handheld mobile solutions.
GNUstep and Cocotron are the two most active Open Source projects which provide Cocoa compatibility. Both target a broad set of features and are more likely to provide compatibility with modern environements. Microsoft's WinObjC bridge is a good option for iOS compatibility on Windows platforms.
Cocotron is the basis for several Mac OS X applications ported to Windows.
GNUstep is a GNU project with a long development history and a wide variety of extensions.
mySTEP is developed for handheld mobile devices, development snapshots are released periodically.
WinObjC implements many of the Core libraries and some Foundation classes underlying Cocoa.