  The generalized connections of the (anti)-de Sitter space symmetry algebra,
which are differential forms of arbitrary degree with values in any irreducible
(spin)-tensor representation of the (anti)-de Sitter algebra, are studied. It
is shown that arbitrary-spin gauge field in (anti)-de Sitter space, massless or
partially-massless, can be described by a single connection. A 'one-to-one'
correspondence between the connections of the (anti)-de Sitter algebra and the
gauge fields is established. The gauge symmetry is manifest and auxiliary
fields are automatically included in the formalism.
