  We discuss the existence of the global attractor for a family of processes
$U_\sigma(t,\tau)$ acting on a metric space $X$ and depending on a symbol
$\sigma$ belonging to some other metric space $\Sigma$. Such an attractor is
uniform with respect to $\sigma\in\Sigma$, as well as with respect to the
choice of the initial time $\tau\in\R$. The existence of the attractor is
established for totally dissipative processes without any continuity
assumption. When the process satisfies some additional (but rather mild)
continuity-like hypotheses, a characterization of the attractor is given.
