Covariant supplementation scheme for infinitely reducible first class constraints

For a rather broad class of dynamical systems subject to mixed fermionic first and second class constraints or infinitely reducible first class constrains (IR1C), a manifestly covariant scheme of supplementation of IR1C to irreducible ones is proposed. For a model with IR1C only, an application of the scheme leads to a system with covariantly splitted and irreducible first and second class constraints. Modified Lagrangian formulations for the Green-Schwarz superstring, Casalbuoni-Brink-Schwarz superparticle and Siegel superparticle, which reproduce the supplementation scheme, are suggested.