The paper discusses orderly and chaotic dynamic responses of simple mechanical structures with clearances and impacting. Experimental results from a simulator of a rotating machine with one loose pedestal are presented, and a summary of analytical results for this case is given. The orderly and chaotic responses obtained through numerical integration are presented in the form of bifurcation diagrams. The second part of the paper discusses an existence of the main and higher order resonances in structures with clearances and impacting, which are excited by external periodic forces. For a one-degree-of-freedom nonlinear system, the application of a discontinuous variable transformation, followed by an averaging method provides analytical formulae describing the system response amplitudes and phases in the proximity of the main and harmonic resonances. A numerical example illustrates the results. The discussed methodology can be generalized for the cases of more complex systems.