  Two classes of multivariate random fields with operator-stable marginals are
constructed. The random fields $\mathbb{X}=\{X(t) : t \in \mathbb{R}^d \}$ with
values in $\mathbb{R}^m$ are invariant in law under operator-scaling in both
the time-domain and the state-space. The construction is based on
operator-stable random measures utilising certain homogeneous functions.
