This paper presents an equilibrium model for a binary-feed two-column parapump where the adsorbents display inverted selectivity towards the solutes, considering no dead volumes and an initial state without solutes. The transient and cyclic steady-state solutions for various cases and sub-cases are provided and the influence of two operational parameters discussed. This system can be operated in order to obtain two, one or no pure products from a binary feed solution and can be tuned to set the products concentration to the desired values. A simultaneous concentration effect is also possible. The influence of the presence of dead volumes or solutes at start-up on the transient separation is also analysed and discussed. (C) 1997 Elsevier Science B.V.