This paper concerns kernel-based interpolation methods for vector data with correlated components. It gives conditions for a matrix kernel to be conditionally positive definite in an appropriate sense. The conditions allow construction of matrix kernels from nonsymmetric mixtures and scalings of scalar kernels. In particular the kernel used to model the influence of component $i$ on component $j$ can be different from that used to model the influence of component $j$ on component $i$. The vector modeling techniques considered are particularly appropriate when there are relatively few measurements of one quantity and relatively many of another “correlated” quantity. The paper concludes with some numerical tests on model problems.