  A new concept of Loday algebroid (and its pure algebraic version - Loday
pseudoalgebra) is proposed and discussed in comparison with other similar
structures present in the literature. The structure of a Loday pseudoalgebra
and its natural reduction to a Lie pseudoalgebra is studied. Further, Loday
algebroids are interpreted as homological vector fields on a `supercommutative
manifold' associated with a shuffle product and the corresponding Cartan
calculus is introduced. Several examples, including Courant algebroids,
Grassmann-Dorfman and twisted Courant-Dorfman brackets, as well as algebroids
induced by Nambu-Poisson structures, are given.
