  The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions
with negative zeros is extended to subharmonic functions in $\mathbb{R}^n,
n\geq 3$. We also show that the existence of the limit $\lim_{\rti} \frac{\log
u(r)}{N(r)}$, where $N(r)$ is the averaged counting function of a subharmonic
function $u$ with the associated masses on a ray implies the regular asymptotic
behavior separately for $u$ and for $N$.
