Bricmont J., Kupiainen A. Universality in blow-up for nonlinear heat equations (85K, Latex) ABSTRACT. We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer $k$, we construct a set of codimension $2k$ in the space of initial data giving rise to solutions that blow-up according to the given profile.