Seidel and Thomas introduced some years ago a notion of a spherical
object in the derived category D(X) of a smooth projective variety X.
We introduce a relative analogue of this notion by defining what does
it mean for an object E of the derived category D(Y x X) of a fiber
product of two schemes X and Y to be spherical over Y. We then
study objects of D(Y x X) which are spherical over Y and orthogonal
over Y, showing them to be characterised by cohomological properties
similar to those in the original definition of a spherical object.