  Let $X_{\alpha}=\{X_{\alpha}(t),t\in T\}$, $\alpha>0$, be an
$\alpha$-permanental process with kernel $u(s,t)$. We show that
$X^{1/2}_{\alpha}$ is a subgaussian process with respect to the metric $\sigma
(s,t)= (u(s,s)+u(t,t)-2(u(s,t)u(t,s))^{1/2})^{1/2}$. This allows us to use the
vast literature on sample path properties of subgaussian processes to extend
these properties to $\alpha$-permanental processes. Local and uniform moduli of
continuity are obtained as well as the behavior of the processes at infinity.
Examples are given of permanental processes with kernels that are the potential
density of transient L\'evy processes that are not necessarily symmetric, or
with kernels of the form $ \hat u(x,y)= u(x,y)+f(y)$, where $u$ is the
potential density of a symmetric transient Borel right process and $f$ is an
excessive function for the process.
