Three kinds of artificial composite material are considered: left-handed materials (LHMs) with both negative permittivity and permeability, negative dielectric permittivity materials (NDPMs), and negative magnetic permeability materials (NMPMs). We study the properties of surface plasmon polaritons (SPPs) for both p and s polarizations at three interfaces of LHM and NDPM, NDPM and NMPM, and LHM and NMPM. We mainly investigate the existence regions, dispersion relations, and excitation of SPPs in different frequency regions and find them to be strongly dependent on the parameters of composite materials across the interface. We also examine the possibility of exciting and observing SPPs by attenuated total reflection.