Based on the generalized Rayleigh-Sommerfeld diffraction integrals,the analytical expression for the 3×3 cross-spectral density matrix of nonparaxial off-axis Gaussian-Schell model (GSM) electromagnetic beams propagating in free space is derived and used to formulate the spectral density (intensity),degree of polarization and spectral degree of coherence of electromagnetic beams at the z plane. Nonparaxial on-axis GSM electromagnetic beams and nonparaxial off-axis Gaussian electromagnetic beams can be treated as special cases of our results. The effect of off-axis parameter,self- and cross-correlation lengths on the intensity,the degree of polarization and the spectral degree of coherence of electromagnetic beams are stressed. The results are illustrated by numerical examples.