  In this paper we study how to attack under the self-similarity hypothesis a
perfect fluid Bianchi I model with variable $G,$and $\Lambda,$ but under the
condition $\operatorname{div}T\neq0.$ We arrive to the conclusion that: $G$ and
$\Lambda$ are decreasing time functions (the sing of $\Lambda$ depends on the
equation of state), while the exponents of the scale factor must satisfy the
conditions $\sum_{i=1}^{3}\alpha_{i}=1$ and $\sum_{i=1}^{3}\alpha_{i}^{2}<1,$
$\forall\omega\in(-1,1) ,$ relaxing in this way the Kasner conditions. We also
show the connection between the behavior of $G$ and the Weyl tensor.
