Let F be a strongly non-lattice distribution function with mean zero variance one, and a finite third moment.Let X1, X2,… be i.i.d. with common distribution function F. Let Sn= X1+ X2+…+ Xnand ξnbe random variables independent of Xn+1, Xn+2,…for n = 1,2,....The main results reported here are two limit theorems (Theorem 3 and Theorem 11) on occupation times for a type perturbed random walks Zn= Sn+ ξnwhen ξn's are slowly changing (also called slowly varying in this paper). A stone type local limit theorem, an Edgeworth expansion and an invariance principle are used in the proofs.