There are three types of multiprocessor operating systems: 1) Each CPU has its own OS, allowing sharing of I/O devices and memory but no sharing of processes or page files. 2) Master-slave has one OS on the master CPU that handles all system calls, balancing processes but becoming a bottleneck for large numbers of CPUs. 3) Symmetric multiprocessors have one shared OS that any CPU can run, balancing processes and memory dynamically but requiring critical regions that don't interfere and avoiding deadlocks when multiple CPUs access shared resources.