  In this paper we introduce the \textit{multivariate} Brownian semistationary
(BSS) processes and study the joint asymptotic behaviour of its realised
covariation using in-fill asymptotics. First, we present a central limit
theorem for general stationary multivariate Gaussian processes, which are not
necessarily semimartingales. Then, we show weak laws of large numbers, central
limit theorems and feasible results for BSS processes. An explicit example
based on the so-called gamma kernels is also provided.
