  We study the Sturm-Liouville problem $-y''-\rho y=0$, $y(0)=y(1)=0$. $\rho$
is a generalized derivative of function $P\in L_2[0,1]$. For self-similar $P$
asymptotic formulas for eigenvalues are obtained. In this paper we consider two
cases of self-similarity of $P$: 1) arithmetic degenerate, and 2)
non-arithmetic.
