  Ercolani and McLaughlin have recently shown that the zeros of the
bi-orthogonal polynomials with the weight
$w(x,y)=\exp[-(V_1(x)+V_2(y)+2cxy)/2]$, relevant to a model of two coupled
hermitian matrices, are real and simple. We show that their argument applies to
the more general case of the weight $(w_1*w_2*...*w_j)(x,y)$, a convolution of
several weights of the same form. This general case is relevant to a model of
several hermitian matrices coupled in a chain. Their argument also works for
the weight $W(x,y)=e^{-x-y}/(x+y)$, $0\le x,y<\infty$, and for a convolution of
several such weights.
