Eckmann , J.-P., Epstein , H., Wayne , C.E. NORMAL FORMS FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS (58K, TeX) ABSTRACT. We begin a study of normal form theorems for parabolic partial differential equations. We show that despite the presence of resonances one can construct a partial normal form for perturbations of the Ginzburg-Landau equation. The normal form transformation is expressed in terms of singular integral operators, whose behavior can be controlled in the appropriate function spaces.