Characteristics of the rectangular waveguides with complex dielectric constant (buried rectangular waveguide with weakly absorptive core,rib waveguide with weakly absorptive substrate,buried rectangular waveguide with gain core and absorptive substrate) are analyzed by perturbation method.Direct solution of the complex eigenvalue equations are taken as standard values and compared with the values obtained by the perturbation theory.Numerical results demonstrate that the perturbation method gives numerical results in excellent agreement with those obtained by direct solutions.