The dynamical characteristics of structures, that could be ill-conditioned, is represented in this paper by a linear multi-degree of freedom canonical model. A time domain identification technique is suggested to estimate the mass, damping and stiffness matrices, in real-time, by using excitation-response measurement records. A singular perturbation technique is used to deal with ill-conditioning of the mass matrix. The least square method is applied to recover the unknown matrices. A numerical example is presented to verify the results. The possibility of applying the proposed technique to offshore towers is indicated.