We investigate the existence of a local time process for a class of discontinuous measure branching processes in R. Formally, the local time process is defined as   where X_s is the measure branching process and δ stands for the Dirac function

Actually, where ϕε is a sequence of nice functions converging as generalized functions to δ. The limit is in the weak topology of Prohorov probability measures. We prove that L(t) exists and it has a cadlag version with Probability 1