  Let $X=\{X(t),t\in\mathrm{R}^N\}$ be a centered real-valued operator-scaling
Gaussian random field with stationary increments, introduced by Bierm\'{e},
Meerschaert and Scheffler (Stochastic Process. Appl. 117 (2007) 312-332). We
prove that $X$ satisfies a form of strong local nondeterminism and establish
its exact uniform and local moduli of continuity. The main results are
expressed in terms of the quasi-metric $\tau_E$ associated with the scaling
exponent of $X$. Examples are provided to illustrate the subtle changes of the
regularity properties.
