Recurrence coefficients of semi-classical orthogonal polynomials (orthogonal polynomials related to a weight function w such that is a rational function) are shown to be solutions of nonlinear differential equations with respect to a well-chosen parameter, according to principles established by D. Chudnovsky and G. Chudnovsky. Examples are given. For instance, the recurrence coefficients in an + 1Pn + 1 (x) = xpn(x) − anpn − 1 (x) of the orthogonal polynomials related to the weight exp () on R satisfy , and an2 satisfies a Painlevé PIV equation.