<p>This paper investigates the complex dynamics of the combined vibrations of the top-tensioned risers in in-line (IL) and cross-flow (CF) directions under the effects of vortices and time-varying tension. The study focuses on the 12 ODE equations for the first three order approximations, which are obtained by using the Galerkin projection method and are the nonlinear system with the Mathieu–van der Pol coupling. The approximate solutions of the first-order mode are studied by the incremental harmonic balance method, and the results are verified by the direct numerical simulation. The complex dynamics of the first three order modes are numerically investigated in a wide range of parameters including the parametric frequency, amplitude ratio of the time varying tension, shedding frequency, and fluid parameters, of which four kinds of resonance conditions between the first order natural frequency and the parametric frequency are investigated. The results show that the high-dimensional system exhibits complex dynamics and the hyperchaotic motions are dominant. The system shows various topologies for different fluid parameters (which are correlated with the time-varying parts of drag and lift coefficients) and modes. The strong complexity and the phase synchronization between the CF displacement and lift coefficient for the first-order mode are found under some parameter conditions. With the increasing of the amplitude ratio, the amplitudes of displacements show different variation trends under four kinds of resonance conditions. The IL displacement is much larger than that in the CF direction and the IL displacement varies significantly under different resonance conditions. The displacements and the time-varying parts of drag and lift coefficients of the first-order modes are primary to the other two modes. The results can be helpful for further dynamic design of the risers.</p>