  In this paper we have applied the generalized Kerr-Schild transformation
finding a new family of stationary perfect-fluid solutions of the Einstein
field equations. The procedure used combines some well-known techniques of null
and timelike vector fields, from which some properties of the solutions are
studied in a coordinate-free way. These spacetimes are algebraically special
being their Petrov types II and D. This family includes all the classical
vacuum Kerr-Schild spacetimes, excepting the plane-fronted gravitational waves,
and some other interesting solutions as, for instance, the Kerr metric in the
background of the Einstein Universe. However, the family is much more general
and depends on an arbitrary function of one variable.
