A design methodology is formulated to reveal the dependence of nonlinear slowmotion dynamics of spread mooring systems (SMS) on mooring line arrangement. For a given SMS configuration, catastrophe sets are developed in the parametric design space showing the dependence of stability boundaries and singularities of bifurcations on design variables. This approach eliminates the need for nonlinear simulations. For general SMS design, however, the designer relies on experience rather than scientific understanding of SMS nonlinear dynamics, due to the high number of design variables. Several numerical applications are used to demonstrate counterintuitive ways of improving SMS dynamics. The SMS design methodology formulated in this paper aims at providing fundamental understanding of the effects of mooring line arrangement and pretension on SMS horizontal plane dynamics. Thus, the first guidelines are developed to reduce trial and error in SMS design. The methodology is illustrated by comparing catastrophe sets for various SMS configurations with up to three mooring lines. Numerous examples for a barge and a tanker SMS which exhibit qualitatively different nonlinear dynamic behavior are provided.