  In the paper we consider singular spectral Sturm--Liouville problem
$-(py')'+(q-\lambda r)y=0$, $(U-1)y^{\vee}+i(U+1)y^{\wedge}=0$, where function
$p\in L_{\infty}[0,1]$ is uniformly positive, generalized functions $q,r\in
W_2^{-1}[0,1]$ are real-valued and unitary matrix $U\in\mathbb C^{2\times 2}$
is diagonal. The main goal is to prove that well-known (for smooth case) facts
about number and distribution of zeros of eigenfunctions hold in general case.
