We study the early stages of flocculation in suspensions of charged colloidal particles in the presence of oppositely charged polyelectrolytes. Absolute aggregation rate constants are determined by time-resolved static and dynamic light scattering. The aggregation rates of amidine and sulfate polystyrene latex particles are measured in the presence of various polyelectrolytes as a function of the polymer dose and ionic strength. The suspension stability sensitively depends on both parameters and is mainly controlled by electrostatic forces. The polymer dose determines the overall particle charge, as revealed by electrophoretic mobility measurements. Near the isoelectric point, one observes fast aggregation, while slow aggregation dominates further away from this point. The ionic strength strongly influences the suspension stability through screening of electrostatic interactions. With increasing ionic strength, the width of the fast aggregation regime increases, and in the slow regime the sensitivity of the rate constant on the polymer dose decreases. In the fast regime, the decrease of the ionic strength leads to a substantial enhancement of the aggregation rate constant. This effect is characteristic for charge patch flocculation and results from the presence of surface charge heterogeneities.