The nonlinear dynamics of bimodular laminated composite conical panels subjected to harmonic excitation is investigated using Bert’s constitutive model and first-order shear deformation theory based finite element. The governing equations of motion are solved to obtain the state vector representing the periodic response by employing shooting technique coupled with Newmark time marching and arc length/pseudo-arc length continuation algorithms. The influence of bimodularity, geometric nonlinearity and curvature on the steady state response characteristics of bimodular material laminated composite conical panels is analyzed for the first time. The through the thickness variations of normal strain/stress, steady state stress history, phase plane plots and frequency spectra are presented to explore the nonlinear periodic response characteristics of bimodular conical panels. The frequency response curves reveal increase in hardening nonlinearity with the increase in bimodularity ratio, load amplitude and semi-cone angle. The frequency response curves tend toward softening nonlinear behavior with the increase in curvature and/or decrease in semi-cone angle.