Pseudospectral (PS) method,whcih has been proven to be very efficient for solving the partial differential equations (PDEs),was combined with the method of lines into the analysis of waveguide problem recent years.This thesis illustrates the pseudospectral method of lines (PMOL) in the hybrid mode analysis by two examples,one is planar structure and the other is cylinder microstrip.PMOL is developed by combining PS technique and the method of lines,therefore its solution not only is analytical along line direction but also maintains high accuracy in discrete direction.The PS Based discretization strategy,distribution of collocation nodes,global power series interpolation of differential quadrature,second-order difference matrix,de-coupling of copuled ordinary differential equations are discussed in details.The second topic of the thesis is to apply a modified Chebyshev PS method with an O(N<-1>) time step restriction to analyze the electromagnetic problem.The extreme eigenvalues of the Chebyshev PS differentiation operator are O(N<2>),where N is the number of grid points.As a result,the allowable time step in an explicit time marching algorithm si O(N<-2>) which in many cases,is much below the time step dictated by the physice of PDE.In this thesis we introduce a new differentiation operator whose eigenvalue are O(N) and the allowable time step is O(N<-1>).The new algorithm is based on interpolating at the zeroes of a parameter dependent,nonperiodic trigonometric function.The properties of the new algorithm are similar to those of the Fourier method but in addition it provides highly accurate solution for nonperiodic boundary value problems.