  In the spiked population model introduced by Johnstone (2001),the population
covariance matrix has all its eigenvalues equal to unit except for a few fixed
eigenvalues (spikes). The question is to quantify the effect of the
perturbation caused by the spike eigenvalues. Baik and Silverstein (2006)
establishes the almost sure limits of the extreme sample eigenvalues associated
to the spike eigenvalues when the population and the sample sizes become large.
In a recent work (Bai and Yao, 2008), we have provided the limiting
distributions for these extreme sample eigenvalues. In this paper, we extend
this theory to a {\em generalized} spiked population model where the base
population covariance matrix is arbitrary, instead of the identity matrix as in
Johnstone's case. New mathematical tools are introduced for establishing the
almost sure convergence of the sample eigenvalues generated by the spikes.
