Photoresponse signals with widths as short as 1.5 ps are observed from epitaxial YBa2Cu3O7−δ thin films using electro‐optic sampling techniques. Voltage transients less than 2 ps wide are seen in 100‐ and 200‐nm films exposed to 150‐fs laser pulses and cooled to 79 K. At low bias currents, the amplitude of the fast response varies linearly with the bias current, suggesting a kinetic inductive mechanism. A negative transient about 15‐ps long is also seen that may provide evidence for nonequilibrium recombination of excited quasiparticles into Cooper pairs. At high bias currents or large laser fluences, a fast tail with a decay time of about 10 ps appears in the response followed by a slow, resistive bolometric component due to sample heating. Nonequilibrium aspects of the photoresponse and the origin of the fast tail are discussed.