A multivariate linear model (Gauss-Markoff model) with noise is used to analyze the estimation of protein secondary structure from spectra of 21 reference proteins whose structures are known from X-ray studies. Fourier transform infrared (FTIR) spectra from 1700 to 1500 cm-1 and circular dichroism (CD) spectra from 178 to 260 nm have been used. The secondary structure categories of interest are alpha-helix, antiparallel beta-sheets, parallel beta-sheets, beta-turns, and "other". The secondary structures are predicted from separate spectra as well as from combined FTIR and CD spectra. The characteristic spectra belonging to the secondary structures and the prediction errors are also estimated. Attention has been paid to the criteria for the choice of rank of matrices of reference spectra, which corresponds to the number of independent pieces of spectral information. Criteria used are: magnitudes of singular values, root mean square error of model fit, relative error of estimable parameters and errors in predicted secondary structure. The ranks of the spectral matrices are found to be between three and six. The model accuracy is determined by removing each protein from the sample and comparing predicted and X-ray values of secondary structure. It is concluded that the linear model is more adequate for the protein FTIR spectra than for the CD spectra. Secondary structure predictions using the FTIR amide I band (1700-1600 cm-1) and the FTIR amide II band (1600-1500 cm-1), or a combination of the two, are of comparable accuracy. In particular, antiparallel beta-sheets and "other" are more reliably estimated from FTIR spectra. However, alpha-helix is more reliably estimated from CD spectra. Combining the spectra yields the best results of both techniques for each class.