Current explanations why a growing economy necessarily goes through periods of high and low growth predict countercyclical R&D investment. As this is very controversial from an empirical perspective, a stochastic Poisson model of endogenous growth cycles is presented where the determinants of the cyclical behaviour of R&D investment are analytically studied. Providing an explicit expression for the expected length of a cycle shows that high frequency fluctuations can indeed be understood by this approach. It is also shown how small technological improvements translate into large aggregate fluctuations.