  The Saffman-Taylor instability occurs when a less viscous fluid is displacing
a more viscous one in a rectangular Hele-Shaw cell. A surface tension on the
interface between the two fluids is improving the stability. The multi-layer
Hele - Shaw model, consisting of $N$ intermediate fluids with constant
viscosities, was studied in some previous papers and very low growth constants
were obtained for large $N$. We prove that this model leads us to a significant
instability, even if $N$ is very large. The maximum value of growth constants
can not decrease under a certain value, not depending on the surface tensions
on the interfaces. This contradiction with the Saffman-Taylor result makes us
have some doubts concerning the correctness of multi-layer model.
