Near-specular scattering (NSS) accompanying a specular beam causes errors in polarimetric measurements, especially for rough surfaces or in the short wavelength region. The Muller matrix for reflection or transmission including the NSS effect will be formulated and analyzed. NSS can cause a polarizer to have slight retardation and nonvanishing extinction ratio. NSS also can cause a retarder to be slightly diattenuated. Null ellipsometry is immune to incoherent and unpolarized NSS, but still cannot avoid partially coherent and polarized NSS. Polarimetric measurements of reflectance or transmittance pick up all types of scattering. NSS can be minimized by keeping the irradiated area and the receiving solid angle as small as possible.