  The linear and non-linear behavior of the top reduced cross section in the
LHeC region is considered concerning the boson-gluon fusion (BGF) model at the
deep inelastic scattering leptoproduction. We will show that the nonlinear
behavior, at this region, for the $t\overline{t}$ production is very small.
Also the behavior of the top reduced cross section and the ratio $R^{t}$ in
this processes is considered.
