Time-domain analytic solutions by operator method for the models described by a set of partial differential equations (models 1 and 2) for unsteady-state mass transfer in a continuous-flow gradientless reactor containing bidisperse porous catalysts are presented. In the models, diffusions in macropores and micropores, adsorption with linear isotherm, and a first-order irreversible reaction are taken into account. Also the input disturbance is allowed to be an arbitrary function of time. The solutions are obtained by self-adjoint formalism in linear operator theory and represented by eigenfunction expansions in an inner product space (Hilbert space). The solutions converge rapidly for typical operating conditions of the reactor, providing a useful means for analyzing as well as designing experiments for estimation of macropore and micropore diffusivities of a biporus catalyst.