The diffraction losses and phase-shifts of TEMpl modes in optical resonators are calculated by quasi-geometric approximation and by the matrix theory (a strict diffraction theory), and the values obtained from the two methods are compared and studied. We come to the following conclusions: (I) The relation of the diffraction losses with the phaseshifts differences between the values obtained from the two methods are close to exponential. (II) When the diffraction losses≥20%, the frequency degeneracy of TEMpl modes may be destroyed in a marked manner, and this would lead to the split of resonant frequency. (III) The exact diffraction loss values calculated from the strict method are nearly linear with the loss values calculated from the approximation method, its slope is b = 0.3559. When the Fresnel number of resonator ?> 2, all the conclusions are independent of mode numbers l, p, and Fresnel number ?. The above mentioned conclusions are obtained only for characteristics of transverse modes, whose losses≤99%, in axial-symmetric stable resonators G2 = G2= 0.5.
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