When structures are subjected to dynamic types of loads, cracks are fairly consistent. Under dynamic loads, such structures exhibit nonlinear and inelastic behaviour. If a suitable load history is taken into account, such structures are assumed to have been fully cracked in flexural tension on top as well as at bottom. This assumption implies that no new cracks will appear when the beam is loaded in the future. As the future loads are assumed not to exceed working load levels, the member behaves as nonlinear-elastic systems. A new class of nonlinear homogeneous dynamical systems has been used to anticipate the dynamical behaviour of the two-DOF cracked concrete beam. This class of systems has a fully nonlinear vibration response that is dependent on the loading details and system parameters of the defined two-DOF dynamical system. In the same way as other nonlinear dynamical systems, concrete beam response has been demonstrated to be extremely sensitive to initial conditions as well as the system parameters and display sub-harmonics. The empirical validity and practical applicability of the proposed theory have been investigated.