We study a generalized version of reversal bounded Turing machines where, apart from several tapes on which the number of head reversals is bounded by r(n), there are several further tapes on which head reversals remain unrestricted, but size is bounded by s(n) (where n denotes the input length). Recently [9,10], such machines were introduced as a formalization of a computation model that restricts random access to external memory and internal memory space. Here, each of the tapes with a restriction on the head reversals corresponds to an external memory device, and the tapes of restricted size model internal memory. We use ST(r(n), s(n), O(1)) to denote the class of all problems that can be solved by deterministic Turing machines that comply to the above resource bounds. Similarly, NST(