We present a formalism that accounts for the interaction of a local quantum system, such as an atom or a cavity, with traveling pulses of quantized radiation. We assume Markovian coupling of the stationary system to the input and output fields and nondispersive asymptotic propagation of the pulses before and after the interaction. This permits derivation of a master equation where the input and output pulses are treated as single oscillator modes that both couple to the local system in a cascaded manner. As examples of our theory, we analyze reflection by an empty cavity with phase noise, stimulated atomic emission by a quantum light pulse, and formation of a Schrödinger-cat state by the dispersive interaction of a coherent pulse and a single atom in a cavity.