Summary: By employing the complex variable method and constructing particular solutions in the form of complex functions, we investigate theoretically the thermal residual stress field near the apex in dissimilar materials bonded with two arbitrary angles, and obtain the corresponding classical solutions. Moreover, the primary paradox, the secondary paradox and even the triple paradox are discovered in classical solutions and also resolved here. Thereby it is confirmed that thermal residual stresses near the apex in bonded dissimilar materials probably possess the singularities of \(\ln r\) (when the primary paradox occurs), \(\ln^2r\) (when the secondary paradox occurs), and even \(\ln^3r\) (when the triple paradox occurs). In addition, we develop a systematic method to solve multiple paradox problems.