The present article provides an analysis of the instants of a system that performs a Newtonian supertask. For each instant it studied the possibility of the system having, from the instant in question, more than one possible course of evolution. This analysis shows that some supertasks presented as deterministic by Pérez Laraudogoitia are in fact indeterministic and specifies the difficulties ahead in showing the radical indeterminism suggested by Atkinson and Johnson.