This investigation presents an approximate method of determining the response of a viscously damped single-degree-of-freedom system exhibiting both in-line (drag) and transverse (lift) flow-induced oscillations. A modified Morison theory is utilized involving the relative system-fluid velocity and accounting for coupling effects between in-line and transverse forcing terms. The method of harmonic balance is adopted to construct a solution of the coupled equations of motion containing periodic terms. Results pertaining to the coupled system are compared with uncoupled results to determine the effect of coupling. Results of the approximate solution are further compared to a numerical time integration of the nonlinear coupled system equations to determine the relative accuracy of the approximate method. Finally, applications to multi-degree-of-freedom methods such as marine riser analysis are discussed.