  For $S$ a positive selfadjoint operator on a Hilbert space, \[
\frac{d^2u}{dt}(t) + 2 F(S)\frac{du}{dt}(t) + S^2u(t)=0 \] describes a class of
wave equations with strong friction or damping if $F$ is a positive Borel
function. Under suitable hypotheses, it is shown that \[ u(t)=v(t)+ w(t) \]
where $v$ satisfies \[ 2F(S)\frac{dv}{dt}(t)+ S^2v(t)=0 \] and \[
\frac{w(t)}{\|v(t)\|} \rightarrow 0, \; \text{as} \; t \rightarrow +\infty. \]
The required initial condition $v(0)$ is given in a canonical way in terms of
$u(0)$, $u'(0)$.
