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The main purpose of this paper is to introduce the notion of anasymptotically almost periodic ultradistribution and asymptotically almostautomorphic ultradistribution with values in a Banach space, as well as tofurther analyze the classes of asymptotically almost periodic andasymptotically almost automorphic distributions with values in a Banach space.We provide some applications of the introduced concepts in the analysis ofsystems of ordinary differential equations.

Asymptotically almost periodic and asymptotically almost automorphic vector-valued generalized functions