  Before we have determined that giant radio structure is typical for
steep-spectrum sources detected with Ukrainian T-shaped Radio Telescope of
model 2 (UTR-2). To estimate the jet propagation velocity and environment
density of giant radio sources we consider the sample of galaxies and quasars
with steep radio spectrum compiled from two regions of UTR-2 catalogue. The
value of velocity of jet propagation is obtained from our estimates of linear
size of radio structure and characteristic age of a source. We use the obtained
values of jet propagation velocity for the estimates of density of jet
environment, that is, density of environment at galaxies and quasars outskirts.
We have derived that values of jet propagation velocities of examined sources
are ~10e9 cm/s. The positive correlation of jet velocity and redshift of
sources is displayed in our sample. On the assumption of equality of jet
luminosity and corresponding kinetic luminosity we estimate the density of jet
environment (radio structure environment) for galaxies (10e-26 gcm-3 to 10e-27
gcm-3) and quasars (10e-28 gcm-3). Considered steep-spectrum galaxies and
quasars display strong evolution of jet propagation velocity and jet
environment density. Properties of giant steep-spectrum sources are in
accordance with conception of long evolution of powerful sources. The steep
low-frequency spectra may be as markers of giant radio structures of galaxies
and quasars.
