  This paper ascertains the global topological structure of the set of
subharmonics of arbitrary order of the periodic predator-prey model introduced
in L\'opez-G\'omez, Ortega and Tineo in 1996. By constructing the iterates of
the monodromy operator of the system, it is shown that the system admits
subharmonics of all orders for the appropriate ranges of values of the
parameters. Then, some sharp results of topological nature in the context of
global bifurcation theory provide us with the fine topological structure of the
components of subharmonics emanating from the T-periodic coexistence state.
