We have studied the vapor-liquid-solid (VLS) growth dynamics of GaP and GaAs in heterostructured GaP-GaAs nanowires. The wires containing multiple GaP-GaAs junctions were grown by the use of metal-organic vapor phase-epitaxy (MOVPE) on SiO(2), and the lengths of the individual sections were obtained from transmission electron microscopy. The growth kinetics has been studied as a function of temperature and the partial pressures of the precursors. We found that the growth of the GaAs sections is limited by the arsine (AsH(3)) as well as the trimethylgallium (Ga(CH(3))(3)) partial pressures, whereas the growth of GaP is a temperature-activated, phosphine(PH(3))-limited process with an activation energy of 115 +/- 6 kJ/mol. The PH(3) kinetics obeys the Hinshelwood-Langmuir mechanism, indicating that the dissociation reaction of adsorbed PH(3) into PH(2) and H on the catalytic gold surface is the rate-limiting step for the growth of GaP. In addition, we have studied the competitive thin layer growth on the sidewalls of the nanowires. Although the rate of this process is 2 orders of magnitude lower than the growth rate of the VLS mechanism, it competes with VLS growth and results in tapered nanowires at elevated temperatures.