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Relaxation oscillation superconducting quantum interference devices (SQUIDs) (ROSs) and double relaxation oscillation SQUIDs (DROSs) have been fabricated and characterized. The SQUIDs are based on hysteretic Nb/Al,AlOx/Al/Nb Josephson tunnel junctions. The relaxation oscillations were simulated by computer. By these simulations the minimum and maximum values of the shunt inductance at which the relaxation oscillations persist have been determined for different values of the shunt resistance and of the critical current and capacitance of the junctions. The transfer from flux to dc voltage in ROSs increases linearly with the shunt resistance. The operation range of the shunt inductance, however, becomes smaller with increasing shunt resistance. In ROSs with a SQUID inductance of 20 pH, a maximum voltage modulation width of 400 μV and a flux-to-voltage transfer δV/δφ of 4 mV/φ0 have been obtained. Two ROSs have been operated in a simple flux-locked loop with direct voltage readout. The experimental white flux noise spectral density of about 3μφ0/√Hz is in good agreement with the theoretical model. The sensitivity of these SQUIDs is limited by so-called switching noise, which is noise due to the interaction between the relaxation oscillations and the Josephson frequency. In DROSs typical flux-to-voltage transfer values of 10–30 mV/φ0 and maximum values up to 80 mV/φ0 have been obtained. This transfer is determined by thermal noise on the critical currents of the SQUIDs. The effective flux noise density of DROSs in flux-locked-loop operation with direct voltage readout is in good agreement with the theoretical noise level which is mainly determined by thermal noise on the critical currents. In one of the DROSs with a SQUID inductance of 20 pH, a white flux noise of 1μφ0/√Hz has been obtained at an estimated relaxation frequency of about 80 MHz. This corresponds to an energy sensitivity of about 160 h.