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 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.