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Semileptonic decays of Λ b and Λ c baryons are studied within the relativistic three-quark model using finite values of heavy quark masses. Employing the same parameters as have been used previously for the description of exclusive decays of heavy baryons in the heavy quark limit we calculate the six form factors of the process and the corresponding decay rates. Our calculation shows that the ''finite mass'' corrections are important in heavy-to-light transitions and are not negligible in heavy-to-heavy transitions.