Modal dynamic substructuring is widely used to perform structural dynamic analysis. Recently, an efficient modal formulation using (free interface) real modes of the substructures has been proposed based on the Udwadia-Kalaba formalism. The latter expresses the subsystems' constrained response from their unconstrained response by explicitly solving the constraining forces. From an experimental point of view, in presence of non-classical damping, the modal formulation based on real modes presents certain difficulties due to its use of the modal damping matrix. The study presents an alternative formulation based on complex modes of the subsystems, requesting only the knowledge of vibration poles and complex mode shapes. As an example of application, the dynamic response of three harps from Central Africa exhibiting strongly complex modes is simulated by assuming both a proportional and non-proportional damping. Significant differences of frequency content are observed due to the absence of coupling by damping between some sets of modes.