In the contemporary literature on Turing machine-based complexity theory, properties of acceptable sets with respect to various factors--such as (1) the machine is a deterministic, nondeterministic, or alternating type; (2) the number of tapes; (3) bounds on the time and space; (4) size of the alphabet set; and (5) the number of states--have been studied. In this paper, using the concept of crossing-sequences and Kolmogorov complexity, a class of separation theorem for one-tape nondeterministic Turing machines with a large (but fixed) number of states is proved. It is shown that a Turing machine with these restrictions can accept more sets in time bound x f ( n ) than in time y f ( n ) where x and y are real, 0 < y < x and f ( n ) is a function with the property that f ( n ) &slash; n log n > 0 and f ( n ) &slash;n ² < ∞ as n → ∞ Since arguments based on crossing sequences don’t readily extend to Turing machines with two or more tapes and for computations requiring more than n ² time, extension of this result to these cases would constitute an interesting open problem.