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We show that bounds on the Castelnuovo-Mumford regularity of singularschemes, as a function of the degrees of the equations defining the shceme, ofits dimension and of the dimension of their singular space. In the case wherethe singularities are isolated, we improve the bound given by Chardin andUlrich, and in the general case we establish a bound doubly exponential in thedimension of the singular space.  --  Nous montrons dans cet article des bornes pour la regularite deCastelnuovo-Mumford d'un schema admettant des singularites, en fonction desdegres des equations definissant le schema, de sa dimension et de la dimensionde son lieu singulier. Dans le cas ou les singularites sont isolees, nousameliorons la borne fournie par Chardin et Ulrich et dans le cas general, nousetablissons une borne doublement exponentielle en la dimension du lieusingulier.

Bornes pour la r\'egularit\'e de Castelnuovo-Mumford des sch\'emas non lisses