We have reevaluated the orbital elements for each pair of the quadruple (W-R+O) + (O+O) stellar system GP Cep and propose new spectral types WN6o/WCE + O3-6, B0: I + B1: V-III. It is shown that there is only one Wolf-Rayet (W-R) star in GP Cep, contrary to a previous claim. A rate of change = 1.3 ± 0.2 s yr-1 is determined for the W-R+O pair, which leads to a new period of 6.6887 days and to a W-R mass-loss rate of (0.8-3.0) × 10-5 M☉ yr-1. Masses for this pair are estimated to be MW-R 6 M☉ and MO 21 M☉. The effects of wind-wind collision in the W-R+O pair are studied. It is shown that even after allowing for dilution by the OB components of the quadruple system, these effects are not as strong as in the binary V444 Cygni (WN5+O6, P = 4.212 days). In GP Cep, the phase-dependent, relatively weak excess emission does not originate in the arms of the bow shock cone. Rather, it emerges from the extra heated portion of the W-R wind facing the hot O companion. The trailing bow shock arm is clearly seen, however, as an enhanced He I absorption component near quadrature at phase ~0.73. An anomalous blueshifted He I absorption is present at phase ~0.9, as is also seen in V444 Cyg, in the WC8+O9 I/O8 III binary γ Velorum and in the LBV-cotype binary R81 (B2.5 Iab:e). A 3.5 day orbit for the eclipsing B star pair is confirmed.
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