The feasibility of using of current-biased superconducting strips for radiation detection is investigated. Narrow Ta strips are exposed to 5.5 MeV α-particle radiation and the rise-time of the induced voltage pulses is measured as function of temperature and bias current. The rise-time of the voltage signal strongly depends on the site on the strip which is hit by the α-particle. In order to determine the spatial resolution of a superconducting strip detector, position-sensitive measurements were performed. The maximum lateral resolution estimated so far is 25 μm in a 7 μm wide, 340 nm thick and 0.6 mm long Ta-strip.