A process for the continuous isomerization of an alkane to produce an isomerized product through contacting the alkane with a simulated moving bed acting as a catalyst for isomerization and an adsorbent for the alkanes has been developed. The alkane may be n-butane and the isomerized product 2-methylpropane, the alkane may be n-pentane and the isomerized product 2-methylbutane or 2,2-dimethylpropane, the alkane may have from 6 up to about 8 carbon atoms with no more than one methyl branch and the isomerized product having the same number of carbon atoms and at least two methyl branches, or the reactant may be a mixture of the foregoing alkanes with the corresponding isomerized products being formed. In a zone of the simulated moving bed, the alkanes are catalytically isomerized to form the isomerized products. The unreacted alkanes are adsorbed, and the isomerized products are collected. In a first subsequent zone of the simulated moving bed, a large portion of the unreacted alkanes are desorbed using a desorbent. In a second subsequent zone of the simulated moving bed, residual adsorbed alkanes are desorbed using a mixture of desorbent and isomerized products, and the desorbed residual alkanes may be removed from the simulated moving bed or may be reacted to form additional isomerized products. The isomerized products are removed from the simulated moving bed and collected. The process may also be used to effect other chemical reactions with the concurrent separation of product.