We present the results of a search for microvariability in a sample of eight Seyfert galaxies. Microvariability (i.e., variations occurring on timescales of tens of minutes to hours) has been conclusively demonstrated to exist in the class of active galactic nuclei (AGNs) known as blazars. Its existence in other classes of AGNs is far less certain. We present the results of a study of eight Seyfert 1 galaxies, which were intensively monitored in order to determine whether such variations exist in these objects. Only one object, Ark 120, displayed any evidence of microvariations. The implications of these results with respect to current models of the mechanisms responsible for the observed emission in Seyfert galaxies are discussed. We compare our results with those obtained from other studies of microvariability in different classes of AGNs.