  Context: New eclipse minimum timings of the M4.5/M4.5 binary CM Dra were
obtained between the years 2000 and 2007. In combination with published timings
going back to 1977, a clear non-linearity in observed-minus-calculated (O-C)
times has become apparent. Several models are applied to explain the observed
timing behavior.
  Aims: Revealing the processes that cause the observed O-C behavior, and
testing the evidence for a third body around the CM Dra system.
  Methods: The O-C times of the system were fitted against several functions,
representing different physical origins of the timing variations.
  Results: An analysis using model-selection statistics gives about equal
weight to a parabolic and to a sinusoidal fitting function. Attraction from a
third body, either at large distance in a quasi-constant constellation across
the years of observations or from a body on a shorter orbit generating
periodicities in O-C times is the most likely source of the observed O-C times.
The white dwarf GJ 630.1B, a proper motion companion of CM Dra, can however be
rejected as the responsible third body. Also, no further evidence of the
short-periodic planet candidate described by Deeg et al. (2000) is found,
whereas other mechanisms, such as period changes from stellar winds or
Applegate's mechanism can be rejected.
  Conclusions: A third body, being either a few-Jupiter-mass object with a
period of 18.5+-4.5 years or an object in the mass range of 1.5M_jup to
0.1M_sun with periods of hundreds to thousands of years is the most likely
origin of the observed minimum timing behavior.
