We examine the processes $e^+ e^-longrightarrow W^+ W^-$ and $Z^0 Z^0$ in the context of the $SP(6)_Lotimes U(1)_Y$ model. We find that there are significant deviations in the total cross sections $sigma (s)$ from the standard model results due to the presence of additional gauge bosons $Z^prime$ and $W^prime$ in the model. These deviations could be detected at LEP.