  We study the decay of large amplitude, almost periodic breather-like states
in a deformed sine-Gordon model in one spatial dimension. We discover that
these objects decay in a staggered fashion via a series of transitions, during
which higher harmonics are released as short, staccato bursts of radiation.
Further, we argue that this phenomenon is not restricted to one particular
model, and that similar mechanisms of radiative decay of long-lived oscillating
states can be observed for a wide class of physical systems, including the
$\phi^6$ model.
