  Kernels of $\alpha$-permanental processes of the form
  \[ v(x,y)=u(x,y)+f(y),\qquad x,y\in S, \]
  in which $u(x,y)$ is symmetric, and $f$ is an excessive function for the
Borel right process with potential densities $u(x,y)$, are considered.
Conditions are given that determine whether $\{v(x,y);x,y\in S\}$ is
symmetrizable or asymptotically symmetrizable.
