Gradient elution chromatography (GEC) is not only commonly used in laboratory settings, but also increasingly used in separation and purification of biochemical and pharmaceutical products. These processes often deal with very precious materials. Thus, it is extremely important to obtain operational conditions so that the process efficiency is optimum. However, this class of optimal control problems is highly nonstandard, and hence cannot be solved using conventional optimal control techniques. There are three specific characteristics associated with this class of optimal control problems : (i) the process contains a set of interrelated subprocesses with different time or space intervals; (ii) the min-max objective function is not in the conventional form; and (iii) state dependent time lag appears in the control variables. This paper considers a related optimal control problem in which optimal control strategies of gradient elution linear chromatography (GELC) are to be obtained for protein separations. The ionic strength, the gradient of which affects the linear equilibrium constants in affinity chromatography systems, is selected as the control variable. Using the control parametrization technique, the control variables are approximated by piecewise linear functions. Thus, a sequence of nonstandard optimal parameter selection problems is obtained. Each of these approximate problems is then shown to be equivalent to a standard min-max optimization problem, and hence is solvable by existing optimization software. For illustration, the proposed methodology is used in a case study.