In order to analyze the characteristic of the close optical axis (conjugate optical axis) and the existence condition of resonator composed of multiple reflective mirrors, the existence condition of conjugate optical axis of the multiple-resonator consisting of many flat mirrors is analyzed and derived from the angle of beam conversion coordinate transformation. The results show that a closed ray axis in resonator with odd number of mirrors can exist only if each mirror is suitably aligned, while a closed ray axis always exists in non-planar resonators with even number of mirrors, and the angle of the cavity conjugate axis direction changes due to the misalignment of different mirrors. Then from the point of view of the optical multi-pass matrix, the incidence direction of the self-conjugate ray of the resonator consisting of spherical mirrors is analyzed. A detailed analysis of conjugated axis of the resonator consisting of two flat mirrors and one spherical mirror is conducted, and the results show that when different mirrors have angle deviations, the closed conjugated optical axis remains in the cavity, the change of resonator axis occurs, and the position and orientation of new resonance surface are given, thereby indicating that in the case of resonator with spherical mirrors there is a self-conjugate ray irrespective of the other flat mirrors positions. All of these will provide theoretical guidance for achieving the high-accuracy alignment and improving the measurement accuracy of spectral measurement technology based on high-quality optical cavity.