[en] The generalized Raychaudhuri equations derived by Capovilla and Guven are exclusively for extremal, timelike Nambu-Goto membranes. In this article, we construct the corresponding equations for string world sheets in the presence of a background Kalb-Ramond field. We analyze the full set of equations by concentrating on special cases in which the generalized shear or the generalized rotation or both are set to zero. If only the generalized shear is set to zero then it is possible to identify the components of the generalized rotation with the projections of the field strength of the Kalb-Ramond potential. copyright 1996 The American Physical Society