Abstract A general free-interface complex component mode synthesis (CMS), which uses truncated component complex modes, complemented with residual flexibility and inertia-relief modes, has been developed and allows assembly of a damped multi-component system with rigid and/or flexible interfaces. In this method, all rigid and flexible-interface co-ordinates are eliminated from the final set of system equations by utilizing the interface compatibility ties. Examples of continuous and discrete damped rotors are used to compare accuracies in frequencies and damping exponents obtained by the complex CMS method to those obtained by the real CMS method at various levels of damping and mode truncations. It is found that sufficiently accurate solutions can be obtained by use of the simpler real CMS method when modal damping ratios of about 70% or less are present. When the modal damping ratios can exceed 70%, use of the complex CMS method is indicated.