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In this paper, the preimage branch t-entropy and entropy dimension for nonau-tonomous systems are studied and some systems with preimage branch t-entropy zero are intro-duced. Moreover, formulas calculating the s-topological entropy of a sequence of equi-continuous monotone maps on the unit circle are given. Finally, examples to show that the entropy dimen-sion of non-autonomous systems can be attained by any positive number s are constructed.