  We present the results of an intensive campaign of spectroscopic and
photometric monitoring of the peculiar Wolf-Rayet star WR 134 from 1989 to
1997.
  This unprecedentedly large data set allows us to confirm unambiguously the
existence of a coherent 2.25 +/- 0.05 day periodicity in the line-profile
changes of He II 4686, although the global pattern of variability is different
from one epoch to another. This period is only marginally detected in the
photometric data set. Assuming the 2.25 day periodic variability to be induced
by orbital motion of a collapsed companion, we develop a simple model aiming at
investigating (i) the effect of this strongly ionizing, accreting companion on
the Wolf-Rayet wind structure, and (ii) the expected emergent X-ray luminosity.
We argue that the predicted and observed X-ray fluxes can only be matched if
the accretion on the collapsed star is significantly inhibited. Additionally,
we performed simulations of line-profile variations caused by the orbital
revolution of a localized, strongly ionized wind cavity surrounding the X-ray
source. A reasonable fit is achieved between the observed and modeled
phase-dependent line profiles of He II 4686. However, the derived size of the
photoionized zone substantially exceeds our expectations, given the observed
low-level X-ray flux. Alternatively, we explore rotational modulation of a
persistent, largely anisotropic outflow as the origin of the observed cyclical
variability. Although qualitative, this hypothesis leads to greater consistency
with the observations.
