The LP (logic of paradox) is a paraconsistent logic. One of the motivationsbehind paraconsistent logic, namely LP, is that it should not allow that everything followsfrom a single contradiction. However it has one important drawback: that some classicalinferences would be invalid in LP. The LP.(logic of minimal paradox) can overcome thisdrawback, such that paraconsistent logic would be equivalent to classical logic when therewas not direct effect of a contradiction. Originally, LP and LP. were only defined in semantic. Although some proof theories for LP were introduced, it has left open how to obtain a satisfactory proof theory for LP.. This paper propose the sound and completestableaux with respect to the semantics of LP and LP., respectively.