  Exterior algebras and differential forms are widely used in many fields of
modern mathematics and theoretical physics. In this paper we define a notion of
$N$-metric exterior algebra, which depends on $N$ matrices of structure
constants. The usual exterior algebra (Grassmann algebra) can be considered as
0-metric exterior algebra. Clifford algebra can be considered as 1-metric
exterior algebra. $N$-metric exterior algebras for $N\geq2$ can be considered
as generalizations of the Grassmann algebra and Clifford algebra. Specialists
consider models of gravity that based on a mathematical formalism with two
metric tensors. We hope that the considered in this paper 2-metric exterior
algebra can be useful for development of this model in gravitation theory.
Especially in description of fermions in presence of a gravity field.
