An object-oriented application programming interface (API) derived from NEXTSTEP and proposed as an open standard by NeXT in 1994.
OpenStep is the specification of the object kits of NEXTSTEP. OPENSTEP/Mach was an implementation of this specification. The original, OPENSTEP version 4.0, and really was NEXTSTEP 4. Rhapsody was the codename for Apple's Mac OS X Server, which is really NEXTSTEP 5 (it calls itself "kernel 5.3" at boot time).
OpenStep was designed to be implemented independently of the computer's operating system, hardware, and user interface. The API for Rhapsody will be a superset of OpenStep's.
When the OpenStep API is implemented for a specific platform and made into a product, it is written in uppercase, e.g. OPENSTEP Developer 4.2 for Mach, or OPENSTEP Enterprise for Windows NT and Windows 95. Versions of OPENSTEP exist for Windows 95/NT, Solaris, HP/UX, and Mach.