The operation of a constant-current quantum interferometer with two Josephson junctions is investigated in a system for measuring small changes in a magnetic field with low-frequency modulation of the magnetic flux. Idealized theoretical signal characteristics are found together with their depedence on the operating mode and parameters of a SQUID. These characteristics are used in Pt. II (ref. 12) to determine the minimal detectable change in the magnetic flux, which characterizes the maximal sensitivity of a SQUID. 12 REFS.