  It is well-known that 0 is the absorbing state for a branching system. Each
particle in the system lives a random long time and gives a random number of
new particles at its death time. It stops when the system has no particle. This
paper is devoted to studying the fixed range crossing numbers until any time t.
The joint probability distribution of fixed range crossing numbers of such
processes until time t is obtained by using a new method. In particular, the
probability distribution of total death number is given for Markov branching
processes until time t.
