Plane Poiseuille flow of viscoelastic liquids of the memory integral type driven by a quasiperiodic pressure gradient, pulsating around a nonzero mean, is investigated. A regular perturbation in terms of a dimensionless amplitude parameter is used. Kernel independent flow enhancement effects are predicted and closed form formulas are given for mass transport rates. Resonance effects are shown to take place. Additional mean flows, independent of the mean pressure gradient, may exist if the frequencies of the superposed waves satisfy certain relationships. An algorithm to determine the constitutive parameters is presented.