A sequence of independent Galton-Watson processes {Xi (t), i≥ 1}, t ? N0= {0, 1,.....} was considered. It was assumed that all the processes have the same offspring distribution. If these processes are looked upon as populations of individuals in different regions, then the above assumptions mean that lives of individuals in different regions are independent and "life conditions" in regions are almost the same. For any fixed t ? N0 let L1 (t) be the index number of the first process such that XL1(t) > 0 and for n= 2,3,. Ln(t)=min {k:k>Ln-1(t), Xk(t)≥X Ln-1(t) (t)} Ln(t), n ≥1, and X Ln(t)(t), n ≥1 are record time processes and upper record value processes. It is known that (see Rahimov [5]) the normalized record value process has the gamma limit distribution of the parameter n as t ∞. Result was established under weaker assumption on offspring distribution and asymptotic behavior of E X Ln(t)(t) as t ∞ was investigated.