Purpose <p>This paper presents a comparative study of the Homotopy Analysis Method (HAM) and Incremental Harmonic Balance Method (IHBM) for solving nonlinear periodic responses in dynamical systems.</p> Methods <p>Both methods are evaluated in terms of accuracy, computational efficiency, convergence behavior, and applicability to strongly nonlinear regimes.</p> Results <p>Numerical results on Duffing and van der Pol oscillators show that IHBM achieves high accuracy and rapid convergence for steady-state solutions, making it well-suited for engineering simulations when adequate harmonic content and good initial guesses are provided. In contrast, HAM offers analytical flexibility and controllable convergence through auxiliary parameters, enabling solution construction even without prior knowledge of periodicity. However, higher-order approximations in HAM incur significant computational cost.</p> Conclusions <p>The results highlight the complementary strengths of the two methods: IHBM excels in efficiency for regular periodic responses, whereas HAM provides greater analytical insight into complex nonlinear dynamics. These findings offer practical guidance for selecting appropriate semi-analytical tools based on problem characteristics.</p>