  We prove a.e. convergence of continuous-time quadratic averages with respect
to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable
measure-preserving $\mathbb{R}^2$-action on a probability space. The key
ingredient of the proof comes from recent work on multilinear singular
integrals; more specifically, from the study of a curved model for the
triangular Hilbert transform.
