For the eclipsing binary system CM Draconis, eclipse minimum times have bee
n monitored with high precision between 1994 and 1999. Periodic deviations
of minimum times from a linear ephemeris may indicate the presence of an or
biting third body. Individual measurements of 41 eclipse minimum times resu
lt in a standard deviation from linear ephemeris of 5.74 seconds. A power s
pectral analysis of the residuals reveals only one periodicity with more th
en 2 seconds amplitude. This feature, with a periodicity between 750 and 10
50 days has an amplitude of 2.8+/-0.5 seconds, and is also present with sim
ilar phases if the power spectral analysis is performed independently fur p
rimary and secondary eclipses. It would be compatible with a circumbinary p
lanet of 1.5 -3 Jupiter masses at an orbital distance of 1.1-1.45 AU to the
binary barycenter. The assignation of a planet to the CM Dra system can ho
wever only be upheld if this periodicity can be followed in future observat
ions for several years. For low-mass eclipsing binary stars, the method of
eclipse minimum timing allows one to reach mass Limits for the detection of
third bodies well below that feasible by radial velocity measurements.