Operating conditions for both the first step and the second step of the two-step process greatly affect alkylate quality and yields; statistical analyses indicate preferred conditions. With n-butenes as olefins, alkylates with research octane number (RON) values in the 99-100.5 range can be produced at operating conditions that are unacceptable in a one-step process. The isoparaffins in the alkylates are produced by three chemical mechanisms, and the relative importance of each differs with the RON of the alkylate.