  We study the growth of a reference network with aging of sites defined in the
following way. Each new site of the network is connected to some old site with
probability proportional (i) to the connectivity of the old site as in the
Barab\'{a}si-Albert's model and (ii) to $\tau^{-\alpha}$, where $\tau$ is the
age of the old site. We consider $\alpha$ of any sign although reasonable
values are $0 \leq \alpha \leq \infty$. We find both from simulation and
analytically that the network shows scaling behavior only in the region $\alpha
< 1$. When $\alpha$ increases from $-\infty$ to 0, the exponent $\gamma$ of the
distribution of connectivities ($P(k) \propto k^{-\gamma}$ for large $k$) grows
from 2 to the value for the network without aging, i.e. to 3 for the
Barab\'{a}si-Albert's model. The following increase of $\alpha$ to 1 makes
$\gamma$ to grow to $\infty$. For $\alpha>1$ the distribution $P(k)$ is
exponentional, and the network has a chain structure.
