Abstract : We consider a Galton-Watson branching process with neutral mutations (infinite alleles model), and we decompose the entire population into sub-families of individuals carrying the same allele. Bertoin has established the description of the asymptotic shape of the process of the sizes of the allelic sub-families when the initial population is large and the mutation rate small. The limit in law is a certain continuous state-space branching process (CSBP). Further, we consider the dierence between the rescaled size of sub-families and corresponding number of mutations. We nd out that it converges in law to some normal distribution with mean zero and whose variance is associated with the CSBP.