  In classical field theory, the composite fibred manifolds Y -> Z -> X
provides the adequate mathematical formulation of gauge models with broken
symmetries, e.g., the gauge gravitation theory. This work is devoted to
connections on composite fibred manifolds. In particular, we get the horizontal
splitting of the vertical tangent bundle of a composite fibred manifold,
besides the familiar one of its tangent bundle. This splitting defines the
modified covariant differential and implies the special fashion of Lagrangian
densities of field models on composite manifolds. The spinor composite bundles
are examined.
