Three kinds of artificial composite materials are involved: left-handed material (LHM), negative dielectric permittivity material (NDPM) and negative magnetic permeability material (NMPM). For the p- and s-polarizations, the properties of surface plasmon polaritons (SPPs) including the existence regions, dispersion relations and excitation of SPPs are investigated in detail in two three-layered asymmetric structures, i.e., dielectric/LHM/NDPM and dielectric/LHM/NMPM. It is found that the properties of SPPs in different frequency regions are strongly dependent on the parameters of composite materials, such as, the slab thickness and plasma frequency for NDPM or LHM. The possibility of exciting and observing SPPs is discussed by attenuated total reflection (ATR) technique. The ATR spectrum is also calculated for p- and s-polarizations cases at these interfaces.