  We report the results of the first two 5 GHz e-VLBI observations of the X-ray
binary Cygnus X-3 using the European VLBI Network. Two successful observing
sessions were held, on 2006 April 20, when the system was in a quasi-quiescent
state several weeks after a major flare, and on 2006 May 18, a few days after
another flare. At the first epoch we detected faint emission probably
associated with a fading jet, spatially separated from the X-ray binary. The
second epoch in contrast reveals a bright, curved, relativistic jet more than
40 milliarcseconds in extent. In the first, and probably also second epochs,
the X-ray binary core is not detected, which may indicate a temporary
suppression of jet production as seen in some black hole X-ray binaries in
certain X-ray states. Spatially resolved polarisation maps at the second epoch
provide evidence of interaction between the ejecta and the surrounding medium.
These results clearly demonstrate the importance of rapid analysis of
long-baseline observations of transients, such as facilitated by e-VLBI.
