An iterative arrays is a line of interconnected interacting finite automata. One distinguished automaton, the communication cell, is connected to the outside world and fetches the input serially symbol by symbol. Sometimes in the literature this model is referred to as cellular automaton with sequential input mode. We investigate deterministic ... iterative arrays (IA) with small time bounds between real-time and linear-time. It is shown that there exists an infinite dense hierarchy of strictly included complexity classes in that range. The result closes the last gap in the time hierarchy of IAs.