  We study a natural generalization of transversally intersecting smooth
hypersurfaces in a complex manifold: hypersurfaces, whose components intersect
in a transversal way but may be themselves singular. Such hypersurfaces will be
called splayed divisors. A splayed divisor is characterized by a property of
its Jacobian ideal. This yields an effective test for splayedness. Two further
characterizations of a splayed divisor are shown, one reflecting the geometry
of the intersection of its components, the other one using K. Saito's
logarithmic derivations. As an application we prove that a union of smooth
hypersurfaces has normal crossings if and only if it is a free divisor and has
a radical Jacobian ideal. Further it is shown that the Hilbert-Samuel
polynomials of splayed divisors satisfy a certain additivity property.
