  We study the limit behavior of the Dirichlet and Neumann eigenvalue counting
function of generalized second order differential operators $\frac{d}{d \mu}
\frac{d}{d x}$, where $\mu$ is a finite atomless Borel measure on some compact
interval $[a,b]$. We firstly recall the results of the spectral asymptotics for
these operators received so far. Afterwards, we give the spectral asymptotics
for so called random recursive Cantor measures. Finally, we compare the results
for random recursive and random homogeneous Cantor measures.
