  We apply a recently developed analytic model for the evolution of monopole
networks to the case of monopoles attached to one string, usually known as
hybrid networks. We discuss scaling solutions for both local and global hybrid
networks, and also find an interesting application for the case of vortons. Our
quantitative results agree with previous estimates in indicating that the
hybrid networks will usually annihilate soon after the string-forming phase
transition. However, we also show that in some specific circumstances these
networks can survive considerably more than a Hubble time.
