  We study the gravitational radiation from a rotating monopole-antimonopole
pair connected by a string. While at not too high frequencies the emitted
gravitational spectrum is described asymptotically by $P_n\propto n^{-1}$, the
spectrum is exponentially suppressed in the high-frequency limit, $P_n\propto
\exp(-n/n_{\rm cr})$. Below $n_{\rm cr}$, the emitted spectrum of gravitational
waves is very similar to the case of an oscillating monopole pair connected by
a string, and we argue therefore that the spectrum found holds approximately
for any moving monopole-string system. As application, we discuss the
stochastic gravitational wave background generated by monopole-antimonopole
pairs connected by strings in the early Universe and gravitational wave bursts
emitted at present by monopole-string networks. We confirm that advanced
gravitational wave detectors have the potential to detect a signal for string
tensions as small as $G\mu\sim 10^{-13}$.
