A method and a corresponding device for bonding a first substrate with a second substrate at mutually facing contact faces of the substrates. The method includes holding of the first substrate to a first holding surface of a first holding device and holding of the second substrate to a second holding surface of a second holding device. A change in curvature of the contact face of the first substrate and/or a change in curvature of the contact face of the second substrate are controlled during the bonding.