  We present the complete family of higher dimensional spacetimes that admit a
geodesic, shearfree, twistfree and expanding null congruence, thus extending
the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations
are solved for empty space with an arbitrary cosmological constant and for
aligned pure radiation. Main differences with respect to the D=4 case (such as
the absence of type III/N solutions, related to ``violations'' of the
Goldberg-Sachs theorem in D>4) are pointed out, also in connection with other
recent works. A formal analogy with electromagnetic fields is briefly discussed
in an appendix, where we demonstrate that multiple principal null directions of
null Maxwell fields are necessarily geodesic, and that in D>4 they are also
shearing if expanding.
