This thesis is divided into two sections, each dealing with the response of a superconducting proximity system to an applied magnetic field. In Section I, the maximum supercurrent that can be carried in an applied perpendicular magnetic field by a supercon- ducting--normal-metal--superconducting (SNS) junction consisting of a square normal-metal layer sandwiched between two crossed perpendicular superconducting strips is investigated theoretically. For weak applied fields, the critical current is suppressed reversibly, as induced Meissner screening currents flow into the SNS sandwich and generate a spatially varying magnetic field largely parallel to the junction, thereby altering the local phase difference. For stronger applied fields, the critical current is changed irreversibly as vortices enter and become pinned in the junction. When the pinned vortices in the two superconductors are misaligned, the local magnetic field, which flows mostly parallel to the junction in carrying magnetic flux from one vortex to the other, strongly alters the phase difference across the junction near the two vortices. The theory predicts com- plex patterns of the supercurrent density, which should be directly observable using laser or electron-based scanning techniques;In Section II, Eilenberger's quasi-classical formulation of superconductivity is used to derive an equation for the upper critical field of a multilayered SN system in a perpendicular magnetic field. The alternating layers are coupled via the proximity effect and are in the dirty limit. Comparison with experimental data for Nb/Cu multilayers shows good agreement only if the mean free paths are substantially smaller than those obtained from longitudinal resistivity;measurements. One feature of this theory is the presence of positive curvature in the upper critical field near the critical temperature; *DOE Report IS-T-1192. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy.