  Reductions of higher tangent bundles of Lie groupoids provide natural
examples of geometric structures which we would like to call higher algebroids.
Such objects can be also constructed abstractly starting from an arbitrary
almost Lie algebroid. A higher algebroid is, in principle, a graded bundle
equipped with a differential relation of special kind (a Zakrzewski morphism).
In the paper we investigate basic properties of higher algebroids and show some
applications. Namely, we develop a geometric framework for variational calculus
on higher algebroids (including both forces and momenta). Such a formalism
covers simultaneously variational problems on higher tangent bundles,
first-order problems on algebroids and higher-order problems reduced by
symmetries.
