Electrical characteristics of Pt/Ti/Pt/Au and Pd/Zn/Pd/Au contacts to p-type InGaAs grown on an InP substrate have been characterized as a function of the doping concentration and the annealing temperature. The Pt/Ti/Pt/Au contacts produced the specific contact resistance as low as $2.3{ imes}10^{-6}{Omega}{cdot}cm^2$, when heat-treated at an annealing temperature of $400^{circ}C$. Comparison of the Pt/Ti/Pt/Au and Ti/Pt/Au contacts showed that the first Pt layer plays an important role in reducing the contact resistivity probably by lowering energy barrier at the metal-semiconductor interface. For the Pd/Zn/Pd/Au contacts, the contact resistivity remained virtually unchanged with increasing annealing temperature. The specific contact resistivity as low as $4.7{ imes}10^{-6}{Omega}{cdot}cm^2$ was obtained. The results indicate that the Pt/Ti/Pt/Au and Pd/Zn/Pd/Au schemes could be potentially important for the fabrication of InP-based optoelectronic devices, such as photodetector and optical modulator.