The maximum order complexity (MOC) of a sequence is a very natural generalization of the well-known linear complexity (LC) by allowing nonlinear feedback functions for the feedback shift register which generates a given sequence. It is expected that MOC is effective to reduce such an instability of LC as an extreme increase caused by the minimum changes of a periodic sequence, i. e. , one-symbol substitution, one-symbol insertion or one-symbol deletion per each period. In this paper we will give the bounds (lower and upper bounds) of MOC for the minimum changes of an m-sequence over GF(q) with period qn-1, which shows that MOC is much more natural than LC as a measure for the randomness of sequences in this case.