  In this article we will consider several phenomenological models for the
Universe with varying $G$ and $\Lambda(t)$, where $G$ is the gravitational
"constant" and $\Lambda(t)$ is a varying cosmological "constant". Two-component
fluid model taken into account. An interaction of the phenomenological form
between a barotropic fluid and a quintessence DE is supposed. Three different
forms of $\Lambda(t)$ will be considered. The problem is analysed numerically
and behavior of different cosmological parameters investigated graphically.
Conclusion and discussions are given at the end of the work. In an Appendix an
information concerning to the other cosmological parameters is presented.
