We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter  that deterministic linear time is distinct from nondeterministic linear time. We show that NT IME(n p log (n)) 6= DT IME(n p log (n)). We show that if the class of multi-pushdown graphs has (o(n); o(n=log(n))) segregators, then NT IME(nlog(n)) 6= DT IME(nlog(n)). We also show that atleast one of the following facts holds - (1) P 6= L , (2) For all polynomially bounded constructible time bounds t, NT IME(t) 6= DT IME(t). We consider the problem of whether NT IME(t) is distinct from NSPACE(t) for constructible time bounds t. A pebble game on graphs is defined such that the existence of a "good" strategy for the pebble game on multi-pushdown graphs implies a "good" simulation of nondeterministic time bounded machines by nondeterministic space-bounded machines. It is shown that there exists a "good" strategy for the pebble game on multi-pushdown graphs i the graphs have sublinear separators. Finally, we show that nondeterministic time bounded Turing machines can be simulated by 4 machines with an asymptotically smaller time bound, under the assumption that the class of multi-pushdown graphs has sublinear separators.