Abstract: Generic transversality in complex geometry.A well known elementary property of pseudo-holomorphic curves in almost complex manifolds is *generic transversality*: simple (i.e. not multiply covered) pseudo-holomorphic maps are transverse (that is, unobstructed) for generic almost complex structures on a given target manifold.The corresponding assertion for complex structures is false, since complex structures have much fewer deformations than almost complex structures.Nevertheless,we show how to rescue the statement by restricting to a small neighborhood of the curves we want to make transverse.