  We demonstrate that in a superconducting multilayered system with alternating
interlayer coupling a new type of nonuniform superconducting state can be
realized under in-plane magnetic field. The Zeeman effect in this state is
compensated by the energy splitting between bonding and antibonding levels.
Such compensation mechanism at low temperature leads to the field-induced
superconductivity. We discuss the conditions for the experimental observation
of the predicted phenomena.
