  The frame-like covariant Lagrangian formulation of bosonic and fermionic
mixed-symmetry type higher spin massless fields propagating on the AdS(d)
background is proposed. Higher spin fields are described in terms of gauge
p-forms which carry tangent indices representing certain traceless tensor or
gamma transversal spinor-tensor representations of the AdS(d) algebra o(d-1,2)
(or o(d,1) for bosonic fields in dS(d)). Manifestly gauge invariant Abelian
higher spin field strengths are introduced for the general case. We describe
the general framework and demonstrate how it works for the mixed-symmetry type
fields associated with the three-cell "hook" and arbitrary two-row rectangular
tableaux. The manifestly gauge invariant actions for these fields are presented
in a simple form. The flat limit is also analyzed.
