Relaxation Oscillation SQUIDs (ROSs) based on 4x4 micrometers 2 Nb/AlOx Josephson tunnel junctions have been fabricated and characterized. A ROS consists of a hysteretic dc SQUID shunted by an inductor L and a resistor R in series to induce the relaxation oscillations. The values of L range from 20 nH up to about 300 nH, whereas the time constant L/R are between 8 and 45 ns. Frequency-flux characteristics have been recorded with the help of a spectrum analyzer, directly connected to the ROS. The relaxation frequencies range from 5 to 180 MHz. The experimental characteristics can be explained very well with a simple model describing the oscillation cycle. The effect of the self-induced magnetic field due to a magnetic coupling between the dc SQUID and the shunt circuit has been studied in detail. The sensitivity of ROSs and DROSs (Double Relaxation Oscillation SQUIDs) improves with increasing relaxation frequency. In (D)ROSs based on unshunted, hysteretic tunnel junction dc SQUIDs, the maximum relaxation frequency and the sensitivity are limited by LC resonances due to the SQUID capacitance and the shunt inductance. It is shown that the relaxation frequency can be increased up to frequencies of the order of 1 GHz if an extra resistor is integrated to damp these resonances. The optimum value of the damping resistor can be obtained from the ROS parameters. For stable operation of a (D)ROS, the shunt resistance should not be too large. The optimum value of this resistance can be calculated from the effective McCumber parameter and the bias current. Theoretically, the sensitivity of a ROS with a SQUID capacitance of 1 pF, a SQUID inductance of 20 pH and a relaxation frequency of 1 GHz equals about 5h, where h is Planck's constant. In a DROS with voltage readout based on similar SQUIDs, the theoretical sensitivity at a relaxation frequency of 1 GHz is 17h, with an estimated flux-to-voltage transfer coefficient of 5 mV/(phi) 0.