This paper considers asymptotic inference in the multivariate BEKK model based on (co-)variance targeting (VT). By definition the VT estimator is a two-step estimator and the theory presented is based on expansions of the modified likelihood function, or estimating function, corresponding to these two steps. Strong consis-tency is established under weak moment conditions, while sixth-order moment restrictions are imposed to establish asymptotic normality. Included simulations indicate that the multivariately induced higher-order moment constraints are necessary