through introducing transformed pupil vector and shifted center of aberration fields vector into the nodal aberration expansions of an axially symmetric optical system, the aberration expression in third order of an off-axis optical system and misaligned off-axis optical system are detailed. nodal aberration characteristics of misaligned off-axis optical system are revealed only by analyzing the pupil decentration vector, aberration fields shifted vector and the aberration coefficients of the axially symmetric optical system. actually, it is well demonstrated that the 3rd spherical aberration, 3rd coma, 3rd astigmatism in a misalignment off-axis system are comparable to the aberrations in a misalignment axially symmetric system. otherwise it will not only induced constant 3rd spherical aberration but also constant 3rd coma and 3rd astigmatism over the field of view, when aligned an off-axis optical system elements with error axial spacing.