Our aim is to establish some sufficient conditions for the oscillation of the second-order quasilinear neutral functional dynamic equation $$ {\left( {p(t){{\left( {{{\left[ {y(t) + r(t)y\left( {\tau (t)} \right)} \right]}^\Delta }} \right)}^\gamma }} \right)^\Delta } + f\left( {t,y\left( {\delta (t)} \right)} \right. = 0,\quad t \in {\left[ {{t_0},\infty } \right)_\mathbb{T}}, $$ on a time scale $ \mathbb{T} $ , where ∣f(t, u)∣ ≥ q(t)∣u β ∣, r, p, and q are real-valued rd-continuous positive functions defined on $$ \mathbb{T} $$ , and γ and β > 0 are ratios of odd positive integers. Our results do not require that γ = β ≥ 1, p ∆(t) ≥ 0, $$ \int\limits_{{t_0}}^\infty {{{\left( {\frac{1}{{p(t)}}} \right)}^{\frac{1}{\gamma }}}\Delta t = \infty, } \quad \quad {\text{and}}\quad \quad \int\limits_{{t_0}}^\infty {{\delta^\beta }(s)q(s){{\left[ {1 - r\left( {\delta (s)} \right)} \right]}^\beta }\Delta s = \infty .} $$ Some examples are considered to illustrate the main results.