  In this paper, we study the pointwise convergence of some continuous-time
polynomial ergodic averages. Our method is based on the topological models of
measurable flows. One of main results of the paper is as follow. Let
$(X,\mathcal{X},\mu, (T^{t})_{t\in \mathbb{R}})$ and $(X,\mathcal{X},\mu,
(S^{t})_{t\in \mathbb{R}})$ be two measurable flows, $a\in \mathbb{Q}$, and
$Q\in \mathbb{R}[t]$ with $\text{deg}\ Q\ge 2$. Then for any $f_1, f_2, g\in
L^{\infty}(\mu)$, the limit \begin{equation*}
  \lim\limits_{M\to\infty}\frac{1}{M}\int_{0}^{M}f_1(T^{t}x)f_2(T^{at}x)g(S^{Q(t)}x)dt
\end{equation*} exists for $\mu$-a.e. $x\in X$.
