  We consider the constraints on string networks with junctions in which the
strings may all be different, as may be found for example in a network of
$(p,q)$ cosmic superstrings. We concentrate on three aspects of junction
dynamics. First we consider the propagation of small amplitude waves across a
static three-string junction. Then, generalizing our earlier work, we determine
the kinematic constraints on two colliding strings with different tensions. As
before, the important conclusion is that strings do not always reconnect with a
third string; they can pass straight through one another (or in the case of
non-abelian strings become stuck in an X configuration), the constraint
depending on the angle at which the strings meet, on their relative velocity,
and on the ratios of the string tensions. For example, if the two colliding
strings have equal tensions, then for ultra-relativistic initial velocities
they pass through one another. However, if their tensions are sufficiently
different they can reconnect. Finally, we consider the global properties of
junctions and strings in a network. Assuming that, in a network, the incoming
waves at a junction are independently randomly distributed, we determine the
r.m.s. velocities of strings and calculate the average speed at which a
junction moves along each of the three strings from which it is formed. Our
findings suggest that junction dynamics may be such as to preferentially remove
the heavy strings from the network leaving a network of predominantly light
strings. Furthermore the r.m.s. velocity of strings in a network with junctions
is smaller than 1/\sqrt{2}, the result for conventional Nambu-Goto strings
without junctions in Minkowski spacetime.
