We present the Maxwell superalgebra, an N = 1 , D = 4 algebra with two Majorana supercharges, obtained as the minimal enlargement of a Poincaré superalgebra containing the Maxwell algebra as a subalgebra. The new superalgebra describes the supersymmetries of generalized N = 1 , D = 4 superspace in the presence of a constant Abelian supersymmetric field strength background. Applying the techniques of nonlinear coset realization to the Maxwell supergroup we propose a new κ -invariant massless superparticle model providing a dynamical realization of the Maxwell superalgebra.