The invention relates to a process for bonding by molecular adhesion of two substrates to one another during which the surfaces of the substrates are placed in close contact and bonding occurs by propagation of a bonding front between the substrates. The invention includes, prior to bonding, a step of modifying the surface state of one or both of the surfaces of the substrates so as to regulate the propagation speed of the bonding front. The surface can be modified by locally or uniformly heating or roughening the surface(s) of the substrate(s).