The apparently single WN 6 type star WR 134 ( HD 191765 ) is distinguished among the Wolf-Rayet star population by its strong , presumably cyclical ( \cal P \approx 2.3 day ) , spectral variations . A true periodicity — which is still very much debated — would render WR 134 a prime candidate for harboring either a collapsed companion or a rotating , large-scale , inhomogeneous outflow . We have carried out an intensive campaign of spectroscopic and photometric monitoring of WR 134 from 1989 to 1997 in an attempt to reveal the true nature of this object . This unprecedentedly large data set allows us to confirm unambiguously the existence of a coherent 2.25 \pm 0.05 day periodicity in the line-profile changes of He II \lambda 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 to investigate ( 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 \lambda 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 .