The interaction between galloping and vortex-induced vibration was experimentally investigated for an infinitely long rectangular cylinder with a side ratio of 3:2, free to vibrate in the transverse mode in smooth flow. This geometry showed strong proclivity to instability and large oscillations occurred also at high Scruton numbers, in a range of flow speeds where no excitation was expected according to the classical theory. A high value of the ratio of the quasi-steady galloping critical wind speed to Karman-vortex resonance velocity is necessary to avoid such a combined instability. Measurements of transverse displacements, velocity fluctuations in the wake of the oscillating body and pressures on its surface highlighted nonlinear features of the fluid-structure coupled system, such as superharmonic resonances and hysteresis. In particular, for low values of the Scruton number, non-negligible excitation was observed at low reduced wind speed due to secondary resonance.