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The paper presents some approximate solutions for the time-dependent analysis of composite steel-concrete beams with flexible shear connectors. These permit evaluating the migration of the stresses from the concrete slab to the steel beam and the increment of the deflections, which occur gradually with time as a result of creep and shrinkage of the concrete part. The mathematical formulation of this problem, which involves a coupled system of three equations, with two being integral-differential-type equations, is reduced to a system of ordinary differential equations by applying the algebraic methods (age-adjusted-effective-modulus, effective-modulus, and mean-stress methods). The simplifications introduced by these methods permit obtaining solutions in closed form, which can be useful for practical applications. The accuracy of the numerical results is successively estimated by comparing these values with those of the exact numerical solution, obtained by employing the numerical algorithm proposed elsewhere using the numerical step-by-step procedures of the general method.