  We study the monotonic behaviour of the zeros of the multiple
Jacobi-Angelesco orthogonal polynomials, in the diagonal case, with respect to
the parameters $\alpha,\beta$ and $\gamma$. We prove that the zeros are
monotonic functions of $\alpha$ and $\gamma$ and consider some special cases of
how the zeros depend on $\beta$, especially in the presence of symmetry. As a
consequence we obtain results about monotonicity of zeros of Jacobi-Laguerre
and Laguerre-Hermite multiple orthogonal polynomials too.
