In this paper we report recent results regarding the nucleation and growth of GaP on Si(001), (111), and (113) surfaces under the conditions of pulsed chemical beam epitaxy using tertiary butylphosphine and triethylgallium as source vapors. The kinetics of nucleation and island growth were monitored in real-time by p-polarized reflectance (PR) and laser light scattering measurements. These measurements were supplemented by ex situ atomic force microscopy and high-resolution transmission electron microscopy studies. We report on the observation of an incubation time, tau(i), which strongly depends on surface orientation with tau(i)(001) < tau(i)(111) < tau(i)(113) and, for a given surface orientation and source vapor flux, decreases with increasing substrate temperature. At time t greater than or equal to tau(i) autocatalytic steps observed in the PR signal are correlated to nucleation and overgrowth of GaP nuclei. In addition, PR reveals changes during GaP growth which result in the deterioration of the previously formed perfect GaP islands that are in registry with the underlying silicon lattice. The change in growth mode may be associated with the formation of stacking faults on faceted GaP islands.