Finding roots of a bivariate polynomial f(x1, x2), over a prime field , is a fundamental question with a long history and several practical algorithms are now known. Effective algorithms for describing the roots modulo pk, k ≥ 2, for any general bivariate polynomial, were unknown until the present paper. The main obstruction is lifting the singular roots to . Such roots may be numerous and behave unpredictably, i.e., they may or may not lift from to .