  We study Nevai's condition that for orthogonal polynomials on the real line,
$K_n(x,x_0)^2 K_n(x_0,x_0)^{-1} d\rho (x)\to\delta_{x_0}$ where $K_n$ is the CD
kernel. We prove that it holds for the Nevai class of a finite gap set
uniformly on the spectrum and we provide an example of a regular measure on
$[-2,2]$ where it fails on an interval.
