Closely spaced cylinder arrays are widely used in offshore platform designs. When subject to random waves and currents, their interactive response behavior is very complicated and perhaps beyond the ability of direct analytical formulations to model their motions. In this study extremal statistics methods were utilized to analyze model basin data that investigated the response behavior of in-line paired and triple deep-water cylinder arrays. The cylinder models used in the model basin experiments were constructed with an ABS outer plastic shell that surrounded an inner steel wire core that could be pretensioned. The cylinder model diameter ratio of the outer shell to steel wire was 4.25 with a slenderness ratio of approximately 1300. The cylinder arrays were pretensioned on the top side and were tested varying pitch to diameter ratios of 3.0, 4.4, and 8.75. The random sea states were simulated using a JONSWAP spectrum. The response time series were investigated using generalized extreme value (GEV) distributions that were fitted to the block maxima that represented the maximum in-line relative displacement between two adjacent tendons. The most appropriate models were selected by comparing their goodness of fit via the Anderson-Darling (AD) test criterion with special attentions paid to their performance in fitting the upper tail of the distribution. The selected models were then used to predict threshold-crossing probabilities of the cylinder array relative response behavior. Both tabular and graphical interpretations of the findings are presented and discussed.