  We introduce a relative version of the spherical objects of Seidel and
Thomas. Define an object E in the derived category D(Z x X) to be spherical
over Z if the corresponding functor from D(Z) to D(X) gives rise to
autoequivalences of D(Z) and D(X) in a certain natural way. Most known examples
come from subschemes of X fibred over Z. This categorifies to the notion of an
object of D(Z x X) orthogonal over Z. We prove that such an object is spherical
over Z if and only if it has certain cohomological properties similar to those
in the original definition of a spherical object. We then interpret this
geometrically in the case when our objects are actual flat fibrations in X over
Z.
