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	   An iterated perturbed random walk is a sequence of point processes defined by the birth times of individuals in subsequent generations of a general branching process provided that the birth times of the first generation individuals are given by a perturbed random walk. We prove counterparts of the classical renewal-theoretic results (the elementary renewal theorem, Blackwell’s theorem, and the key renewal theorem) for the number of  j th-generation individuals with birth times  			 		 $\leq t$ 		, when  			 		 $j,t\to\infty$ 		and  			 		 $j(t)={\textrm{o}}\big(t^{2/3}\big)$ 		. According to our terminology, such generations form a subset of the set of intermediate generations.

Renewal theory for iterated perturbed random walks on a general branching process tree: intermediate generations