Abstract
Infinite time register machines(ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands. At limit times a register content is defined as a $\liminf$ of previous register contents, if that limit is finite; otherwise the register is resetto 0. (A previous weaker version of infinitary register machines, in [6], would halt without a result in case of such an overflow.) The theory of infinite time register machines has similarities to the infinite time Turing machines (ITTMs) of Hamkins and Lewis . Indeed ITRMs can decide all $\Pi^1_1$ sets, yet they are strictly weaker than ITTMs.
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