In this paper, we pursue the goal of automatic deductive verification for certain classes of ASM. In particular, we base our work on a translation of general ASMs to full first-order temporal logic. While such a logic is, in general, not finitely axiomatisable, recent work has identified a fragment, termed the monodic fragment, that is finitely axiomatisable and many of its subfragments are decidable. Thus, in this paper, we define a class of monodic ASMs whose semantics in terms of temporal logic fits within the monodic fragment. This, together with recent work on clausal resolution methods for monodic fragments, allows us to carry out temporal verification of monodic ASMs. The approach is illustrated by the deductive verification of FloodSet algorithm for Consensus problem, and Synapse N+1 cache coherence protocol; both are specified by monodic ASMs.