Summary: In this paper, we deal with the asymptotics and oscillation of the solutions of higher-order nonlinear dynamic equations with Laplacian and mixed nonlinearities of the form \[ \begin{aligned} &\bigl\{ r_{n-1}(t) \phi_{\alpha_{n-1}} \bigl[\bigl(r_{n-2}(t) \bigl(\cdots\bigl(r_{1}(t) \phi_{\alpha_{1}} \bigl[x^{\Delta}(t) \bigr] \bigr)^{\Delta}\cdots\bigr)^{\Delta} \bigr)^{\Delta } \bigr] \bigr\} ^{\Delta} \\& +\sum_{\nu=0}^{N}p_{\nu} ( t )\phi _{\gamma _{\nu}} \bigl( x \bigl(g_{\nu}(t) \bigr) \bigr) =0 \end{aligned} \] on an above-unbounded time scale. By using a generalized Riccati transformation and integral averaging technique we study asymptotic behavior and derive some new oscillation criteria for the cases without any restrictions on \(g(t)\) and \(\sigma(t)\) and when \(n\) is even and odd. Our results obtained here extend and improve the results of D.-X. Chen and P.-X. Qu [J. Appl. Math. Comput. 44, No. 1–2, 357–377 (2014; Zbl 1303.34073)] and S. Y. Zhang et al. [“Asymptotics and oscillation of \(n\)th-order nonlinear dynamic equations on time scales”, Appl. Math. Comput. 275, 324–334 (2016; doi:10.1016/j.amc.2015.11.084)].