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Vortex-structure interaction models are studied in the work presented here. The third- order model by Hartlen and Currie (HC model) can reproduce the correct response amplitude, while a fifth-order model by Landl predicts the observed hysterisis effect. Using concepts from nonlinear dynamics and bifurcation theory, the range of possible dynamics of the models is investigated in parameter space; essentially, a class of nonlinear oscillators deriving “naturally” from the HC model is studied. It is found that perturbations of the HC model in parameter space lead to qualitatively physically meaningful dynamics. Forced excitation of the HC model is the highlight of the work. In this case, it is shown that a subharmonic lock-in predicted by the model may be related to a three-dimensional secondary subharmonic instability of a periodic flow. Experimental results are presented for comparison.