We introduce the concept of almost thick chaos and continuously almost thick transitivity for continuous maps and nonautonomous dynamical systems (NDS). We show that NDS f1,∞ is sensitive if it is thick transitive and syndetic. Under certain conditions, we show that NDS (X, f1,∞) generated by a sequence (fn) of continuous maps on X converging uniformly to f is almost thick transitive if and only if (X, f) is almost thick transitive. Moreover, we prove that if f1,∞ is continuously almost thick transitive and syndetic, then it is strongly topologically ergodic. In addition, the relationship between the large deviations theorem and almost thick chaos is studied.

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