Slow‐wave propagation of electromagnetic waves in transmission lines formed of thin‐film superconductors has been studied theoretically and experimentally. Previous theoretical analyses have been extended to include nonlocal theories. Strong dependence of phase velocity is found on film thickness and interfilm spacing when these become less than a few penetration depths. Velocity is also modified by coherence length, mean free path, nature of reflection of electrons at the film surfaces, and by temperature and magnetic field. Experimental measurements were made to verify the dependence on thickness, spacing, and temperature by means of a resonance technique. Agreement with theory was excellent in the case of temperature. Data taken for varying thickness and spacing verified the general trend of theoretical predictions. They indicate a nonlocal behavior with some specular reflection, but scatter of the data taken for different films prevents precise comparison of theory and experiment. Estimates of bulk penetration depths were made for indium, &lgr;In= 648±130 Å. For tantalum a rough estimate could be made of &lgr;Ta= 580 Å. Data were consistent with the estimate of coherence length for indium of &xgr;0≈ 3000 Å. Velocity was found to be independent of frequency in the range 50–500 MHz, while losses increased as the square. Pulse measurements indicated that delays of several microseconds and storage of several thousand pulses on a single line are feasible.