POSIX

Integrity
Secure, no royalty, for high reliability embedded systems; hardware memory protection to isolate and protect it and user tasks from incorrect operation by errors or tampering; object-oriented design allows verifying data security/integrity, communications, individual components, whole system; strict adherence to provable resource requirements. Green Hills Software, Inc.
http://www.ghs.com/products/rtos/integrity.html

Integrity (Operating System)
Growing article, with links to many related topics. Wikipedia.
http://en.wikipedia.org/wiki/Integrity_(operating_system)

MaRTE OS
Realtime kernel for embedded uses, follows Minimal Real-Time POSIX.13 subset. Most code is Ada, but some C, assembly. Hardware access via Abstract Hardware Interface (HAL). Runs in cross development environment: PC Linux Host, bare 386 PC Target, Ethernet LAN link. [Open Source, GPL]
http://marte.unican.es/

REAL/IX PX
A POSIX real-time operating system for x86/Pentium based systems. By Modcomp, Inc.
http://www.modcomp.com/realtime/products/descriptions/8272.html

S.Ha.R.K.
Dynamic configurable kernel architecture to support hard/soft/non realtime use with interchangeable scheduling algorithms: fully modular in scheduling policies, aperiodic servers, concurrency control protocols; all not modular in most traditional OSs. Derived from HARTIK: HArd Real TIme Kernel. [Open Source, GPL]
http://shark.sssup.it/