Let X be a smooth complexe projective variety. A curve C of X isomorphic
to P1 is called a quasi-line if its normal bundle decomposes as as a sum
of \O_{P1}(1). A variety containing a quasi-line is a particular case of a
rationally connected variety. I show that a rationally connected variety
contains a quasi-line after a sequence of blowing ups with smooth centers.
I study the geometry of these varieties:  stability under small
deformations, existence of a numerical invariant characterising the
rationality...