  We show that dressing of diatomic molecules by running laser waves gives rise
to conical intersections (CIs). Due to presence of such CIs, the rovibronic
molecular motions are strongly coupled. A pronounced impact of the CI on the
spectrum of $Na_2$ molecule is demonstrated via numerical calculation for weak
and moderate laser intensity, and an experiment is suggested on this basis. The
position of the light induced CI and the strength of its non-adiabatic
couplings can be chosen by changing the frequency and intensity of the used
running laser wave. This offers new possibilities to control the photo-induced
rovibronic molecular dynamics.
