  We introduce the concept of a higher algebroid, generalizing the notions of
an algebroid and a higher tangent bundle. Our ideas are based on a description
of (Lie) algebroids as vector bundle comorphisms - differential relations of a
special kind. In our approach higher algebroids are vector bundle comorphism
between graded-linear bundles satisfying natural axioms. We provide natural
examples and discuss applications in geometric mechanics.
