AbstractPreviously, we proposed a (k, l)‐neighborhood template δ‐type bounded cellular acceptor (abbreviated as δ‐‐BCA (k, l)), which is composed of a pair of converters and a configuration‐reader and operates on a two‐dimensional tape. Its basic properties have already been discussed. δ‐BCA (k, l) is a parallel automaton, which, in a sense, is a generalization of the one‐dimensional bounded cellular acceptor. This paper attempts a more detailed examination of the properties of δ‐BCA (k, l), and compares its accepting power with those of other automata operating on the two‐dimensional tape. The objects of comparison are the various kinds of two‐dimensional finite automata and various kinds of parallel sequential array acceptors. It is known that there exists an equivalent tape‐bounded Turing machine for each of these automata in the sense of the accepting power. Consequently, the comparison of the accepting power of δ‐BCA (k, l) and those of two‐dimensional automata amounts in a sense to the evaluation of the accepting power of δ‐BCA (k, l) in terms of the tape complexity of the tape‐bounded Turing machine.