The present paper is devoted to computational methods of solving spectral problems for polynomial and rational matrices of general form (regular and singular) dependent on one or two parameters. These problems are as follows: for one-parameter matrices,
• computation of all or a part of the singular points (zeros and poles) and the corresponding structural indices, eigenvectors, and Jordan chains;
t computation of polynomial solutions, minimal indices, and minimal bases of the null-spaces of polynomial solutions; for two-parameter matrices,
• separation of the continuous and discrete spectra;
• computation of the points of the discrete spectrum of a matrix and the corresponding eigenvectors and Jordan chains;
• computation of polynomial solutions, minimal indices, and minimal bases of the null-spaces of polynomial solutions.