The precise character of the quasi-periodic variation in the recurrence of El Ni¿o events has been unclear. To gain insight into the nature of this apparent regularity, a 464-year record (1525--1988) of the initiation of ''strong'' El Ni¿o events, derived from the chronology of the Quinn et al. [1987>, has been analyzed with a two-dimensional extension of the periodogram analysis method of Buys Ballot. The method is useful for detecting joint nonlinear interactions between variations at two specified periods. Results indicate joint nonrandom recurrence of strong El Ni¿o events at periods of 6.75 and 14.0 years. From Monte Carlo tests, we estimate the statistical significance of this result to be at the 0.1% level. Alternating ~95 year-long time-blocks, where 6.75-year and 14.0-year recurrence periods dominate, is apparent from the analysis. No specific mechanism is offered for the periodic forcing of strong El Ni¿o events, but our observation of significant quasi-periodic behavior in the initiation of such events at the combined periods of 6.75 and 14.0 years may be a useful clue in efforts to understand and model natural ENSO recurrence. ¿ American Geophysical Union 1989