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We report the time-domain analysis of fast pulses emitted by a quantum cascade laser (QCL) operating at ~ 3.1 THz using superconducting THz detectors made from either NbN or YBa2Cu3O7-δ (YBCO) thin films. The ultrafast response from these detectors allows resolution of emission features occurring on a nanosecond time-scale, which is not possible with commercially available Ge or InSb bolometers owing to their much larger time constants. We demonstrate that the time-dependent emission can be strongly affected by relatively small variations in the driving pulse. The QCL output power-current relationship was determined, based on correlation of the time-dependent emission of radiation with current flow in the QCL, under different QCL bias conditions. We show that this relationship differs from that obtained using bolometric detectors that respond only to the integrated pulse energy. The linearity of the detectors, and their agreement with measurements using a Ge bolometer, was also established by studying the QCL emission as a function of bias voltage and excitation pulse length. This measurement scheme could be readily applied to the study of ultrafast modulation and mode-locking of THz-QCLs.