In this study a new two degrees-of-freedom wake oscillator model is proposed to describe vortex-inducedvibrations of elastically supported cylinders capable of moving in cross-flow and in-line directions. Totalhydrodynamic force acting on the cylinder is obtained here as a sum of lift and drag forces, which are definedas being proportional to the square of the magnitude of the relative flow velocity around the cylinder. Thetwo van der Pol type oscillators are then used to model fluctuating drag and lift coefficients. As the relativevelocity around the cylinder depends both on the fluid flow velocity and the velocity of the cylinder, theequations of motions of the cylinder in cross-flow and in-line directions become coupled through the fluidforces. It is shown that such approximation of the fluid forces allows to obtain the well known low dimensionalmodels in the limit case, and the model proposed by Facchinetti et al.  to describe the cross-flow vibrationsis used as an example. Experimental data and Computational Fluid Dynamics (CFD) results are used tocalibrate the proposed model and to verify the obtained predictions of complex fluid-structure interactionsfor different mass ratios. A number of phenomena such as the ”super-upper” branch, exclusive for a twodegrees-of-freedom motion at low mass ratios, are observed. Influence of the empirical parameters of thewake oscillators equations and fluid forces coefficients on the response is also discussed.