Analytical expressions for the cross-spectral density and intensity of two-dimensional nonparaxial partially coherent Hermite-Gaussian （H-G） beams in coherent and incoherent additions are derived, and some special cases are analyzed. The intensity of the resulting beam depends not only on the f-parameter, fσ-parameter, off-axis distances, beam numbers and orders of combined beams and propagation distance, but also on the addition scheme. The meaning of the terminology of coherent and incoherent addition of partially coherent beams is interpreted physically and the validity is confirmed by numerical examples.