  We study several cosmological models with Bianchi \textrm{VI}$_{0}$
symmetries under the self-similar approach. In order to study how the
\textquotedblleft constants\textquotedblright\ $G$ and $\Lambda$ may vary, we
propose three scenarios where such constants are considered as time functions.
The first model is a perfect fluid. We find that the behavior of $G$ and
$\Lambda$ are related. If $G$ behaves as a growing time function then $\Lambda$
is a positive decreasing time function but if $G$ is decreasing then $\Lambda$
is negative. For this model we have found a new solution. The second model is a
scalar field, where in a phenomenological way, we consider a modification of
the Klein-Gordon equation in order to take into account the variation of $G$.
Our third scenario is a scalar-tensor model. We find three solutions for this
models where $G$ is growing, constant or decreasing and $\Lambda$ is a positive
decreasing function or vanishes. We put special emphasis on calculating the
curvature invariants in order to see if the solutions isotropize.
