  We describe the Lie algebra deformations of D=4 Maxwell superalgebra that was
recently introduced as the symmetry algebra of a kappa-symmetric massless
superparticle in a supersymmetric constant electromagnetic background. Further
we introduce the D=3 Maxwell superalgebra and present all its possible
deformations. Finally the deformed superalgebras are used to derive via a
contraction procedure the complete set of Casimir operators for D=4 and D=3
Maxwell superalgebras.
