Superconducting films of YBa2Cu3O7-s are shown to become thermomagnetically unstable when experiencing a time-varying perpendicular magnetic field. Using magneto-optical imaging and ramping the applied field at rates up to 3000 T/s, dendritic flux avalanches were observed in two different films, one grown by evaporation on sapphire and one by laser ablatin on SrTiO3. The unstable behaviour occurs over a wide temperature range limited by an upper threshold value of 40 K for the film on sapphire , and 20K for the one on SrTiO3. At 7 K for the same films, the threshold ramping rates are 1000 T/s and 3000 T/s, respectively. The avalanches are causing permanent damage by leaving a micron wide track where the superconductor melted during the thermomagnetic runaway.