  We present the results of a four-month, spectroscopic campaign of the
Wolf-Rayet dust-making binary, WR137. We detect only small-amplitude, random
variability in the CIII5696 emission line and its integrated quantities (radial
velocity, equivalent width, skewness, kurtosis) that can be explained by
stochastic clumps in the wind of the WC star. We find no evidence of
large-scale, periodic variations often associated with Corotating Interaction
Regions that could have explained the observed intrinsic continuum polarization
of this star. Our moderately high-resolution and high signal-to-noise average
Keck spectrum shows narrow double-peak emission profiles in the Halpha, Hbeta,
Hgamma, HeII6678 and HeII5876 lines. These peaks have a stable blue-to-red
intensity ratio with a mean of 0.997 and a root-mean-square of 0.004,
commensurate with the noise level; no variability is found during the entire
observing period. We suggest that these profiles arise in a decretion disk
around the O9 companion, which is thus an O9e star. The characteristics of the
profiles are compatible with those of other Be/Oe stars. The presence of this
disk can explain the constant component of the continuum polarization of this
system, for which the angle is perpendicular to the plane of the orbit,
implying that the rotation axis of the O9e star is aligned with that of the
orbit. It remains to be explained why the disk is so stable within the strong
ultraviolet radiation field of the O star. We present a binary evolutionary
scenario that is compatible with the current stellar and system parameters.
