An isothermal equilibrium theory analysis of a simple two-step pressure-swing adsorption (PSA) process utilizing an adsorbate-adsorbent system that exhibits an unfavorable Langmuir isotherm was carried out. Analytical expressions that directly describe the approach to periodicity as a function of the cycle number were obtained and used to derive expressions for all of the important process performance indicators that change with the cycle number for the case with breakthrough of the heavy component into the light product (i.e., gamma < 1). This PSA process goes through four unique stages on the approach to the periodic behavior that are marked by different shock and simple wave interactions. The most unusual wave interaction that was found occurs between two simple waves and a shock wave that manifests and disappears before the periodic state is reached. A case study with a H-2-metal hydride system that exhibits an unfavorable Langmuir isotherm was used to reveal this unique behavior. This system was also used to show which process performance indicators are a function of the cycle number and how they change as periodicity is approached.