BeOS was definitely a real time OS. BeOS had two scheduling classes, threads with a priority level between 1-99 were time shared threads where the quantum was proportional with 2^priority_level, threads with a priority level between 100 and 120 were real time threads, they could preempt any other thread, including any kernel thread, they were locked to a CPU and never preempted. And when a real time thread was created, it preempted any time shared thread immediately, the scheduler run at creation, it wasn't only added to a scheduling queue like time shared threads.

QNX is a still very popular realtime OS in the embedded world today. Btw, the OS run by the BlackBerry devices is QNX. Usually you'll find QNX in control systems like avionics.