We present separation results on genuinely (or strongly) time bounded sequential, parallel and non-deterministic complexity classes defined by RAMs with fixed set of arithmetic operations. In particular, we separate non-uniform polynomial time from non-uniform parallel polynomial time for the set of operations $\{+,-,*\}$ (answering a question of \cite{M 88}), and uniform deterministic polynomial time from uniform non-deterministic polynomial time for the set of operations $\{+,-,{\mathit DIV}_c\}$, where {\it DIV}$_c$ denotes a restricted integer division operation.