  The electromagnetic decay and final annihilation of magnetic
monopole-antimonopole pairs formed in the early universe has been proposed as a
possible mechanism to produce the highest energy cosmic rays. We show that for
a monopole abundance saturating the Parker limit, the density of magnetic
monopolonium formed is many orders of magnitude less than that required to
explain the observed cosmic ray flux. We then propose a different scenario in
which the monopoles and antimonopoles are connected by strings formed at a low
energy phase transition (~ 100 GeV). The bound states decay by gravitational
radiation, with lifetimes comparable with the age of the universe. This
mechanism avoids the problems of the standard monopolonium scenario, since the
binding of monopoles and antimonopoles is perfectly efficient.
