  Variability of the spin period of the white dwarf in the V405 Aur (RX
J0558.0+5353) system using our observations and previously published maxima
timings is analyzed. As the phase light curve contains two nearly equal
photometric waves, one maximum was set as a "primary" one. The ephemeris for
the maxima of the "spin variability" (due to rotation of the magnetized white
dwarf) for recent seasons 2010-2012 is Tmax = HJD
2455882.470614(25)+0.00631314602(46)E. This corresponds to a significant
negative trend at the "O-C" diagram. Due to significant gaps in the
observational data and statistical error of timings, there may be some
suggestions on the spin period variability - a fast period "jump" in 2007y;
secular period variations; a cubic ephemeris (which may be interpreted by a
precession of the magnetic white dwarf at a time-scale of decades) or a
periodic change with a period of 6.2 years and semi-amplitude of 17.2\pm1.8
sec. For the present observations, more reliable are two latter models. To
distinguish between them, a continuation of monitoring is needed. The periodic
variations may be interpreted by a light time effect caused by a third body of
mass (M3 > 0.09M\odot), which corresponds to a low-mass star, but not to an
extra-solar planet. In this case, the system belongs to a rare class of
cataclysmic variables with a third body.
