  Quark and gluon parton dihadron fragmentation functions and their evolution
are studied in the process of e+e- annihilation. We provide definitions of such
dihadron fragmentation functions in terms of parton matrix elements and derive
the momentum sum rules and their connection to single hadron fragmentation
functions. We parameterize results from the Lund Monte Carlo model JETSET as
the initial conditions for the parton dihadron fragmentation functions at the
scale Q_0^2=2 GeV^2. The evolution equations for the quark and gluon
fragmentation functions are solved numerically and the results at different
higher scales Q^2 agree well with JETSET results. The importance of the input
from the single fragmentation functions is pointed out.
