  Let $(A,\mathfrak{m})$ be a local complete intersection ring and let $I$ be
an ideal in $A$. Let $M, N$ be finitely generated $A$-modules. Then for $l =
0,1$, the values $depth \ Ext^{2i+l}_A(M, N/I^nN)$ become independent of $i, n$
for $i,n \gg 0$. We also show that if $\mathfrak{p}$ is a prime ideal in $A$
then the $j^{th}$ Bass numbers $\mu_j\big(\mathfrak{p},\
Ext^{2i+l}_A(M,N/{I^nN})\big)$ has polynomial growth in $(n,i)$ with rational
coefficients for all sufficiently large $(n,i)$.
