  We study weak asymptotic behaviour of the Christoffel--Darboux kernel on the
main diagonal corresponding to multiple orthogonal polynomials. We show that
under some hypotheses the weak limit of $\tfrac{1}{n} K_n(x,x)\, d\mu$ is the
same as the limit of the normalized zero counting measure of type II multiple
orthogonal polynomials. We also study an extension of Nevai's operators to our
context.
