High‐resolution electron‐beam lithographic techniques have been used in the fabrication of thin ultranarrow superconducting Nb stripes. The ac Josephson effect in the form of microwave‐induced current steps has been observed in a series of samples in which the length has been varied from about 1 to 0.1 &mgr;m. Studies of the phase slip centers in these samples have led to an estimate for the quasiparticle diffusion length and inelastic scattering time of about 90 nm and 13 ps, respectively.