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The Lagrangian and Hamiltonian functions describing average motion of arelativistic particle under the action of a slightly inhomogeneous intenselaser field are obtained. In weak low-frequency background fields, such aparticle on average drifts with an effective, relativistically invariant mass,which depends on the laser intensity. The essence of the proposed ponderomotiveformulation is presented in a physically intuitive and mathematically simpleform, yet represents a powerful tool for studying various nonlinear phenomenacaused by interaction of currently available smooth ultra-intense laser pulseswith plasmas

Drift Lagrangian for a relativistic particle in an intense laser field