Cellular automata are widely used to model natural systems. Classically they are run with perfect synchrony, {\em i.e.}, the local rule is applied to each cell at each time step. A possible odification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For some particular rules, varying the synchrony rate continuously produces a discontinuity in the behaviour of the cellular automaton. We investigate the nature of this change of behaviour using Monte-Carlo simulations. We apply a two-step protocol to show that the change of behaviour is a phase transition whose critical exponents are in good agreement with the predicted values of directed percolation and parity conservation universality classes.