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We generalize Stark-chirped rapid adiabatic passage to the case of a multilevel atom. The atom is assumed to have two ground state levels g and f and an excited level e. The adiabatic passage is carried out by resonantly driving the g-e and f-e transitions with time-dependent pump and Stokes fields in the presence of strong far-off-resonant Stark field. Our formalism determines the states that participate in population transfer and is applicable to systems with arbitrary numbers of degenerate states in each level and arbitrary couplings of the g-e and f-e transitions. We give an application to adiabatic passage in Rb atom.