The phase and spectral characteristics of long-period geomagnetic pulsation wave trains consisting of two overlapping responses to independent excitations are investigated. The major purposes of the work are to expand diagnostic processes in pulsation analysis and to use these techniques to determine the phase and spectral characteristics of these wave trains. It is shown that the inherent phase and amplitude modulation in such wave trains can significantly alter the power spectrum and can introduce either a phase jump or a phase skip. When the two individual responses have the same underlying (carrier) frequency, the spectral peak or peaks of the composite wave train can be offset from the carrier frequency, and these offsets are associated with a phase jump or skip. These phase and spectral characteristics are dependent on the difference in phase between the two responses and on the extent of their overlap. Analytic signal representation of our modeled wave trains yields more accurate estimates of the underlying pulsation frequency than do the power spectra. When the frequencies of the two responses differ, the phase and spectral characteristics become more complex. Finally, the analytic approach is applied to a real pulsation event.