  The influence of uniform pressures $P$ up to 5 kbar on the superconducting
transition temperature $T_c$ was studied for the FeSe$_{1-x}$Te$_x$ ($x=0$,
0.85, 0.88 and 0.9) system. For the first time, we observed a change in sign of
the pressure effect on $T_c$ when going from FeSe to tellurium rich alloys.
This has allowed to specify the pressure derivative d$T_c$/d$P$ for the system
as a function of composition. The observed dependence was compared with results
of the {\em ab initio} calculations of electronic structure and magnetism of
FeSe, FeTe and FeSe$_{0.5}$Te$_{0.5}$, and also with our recent experimental
data on pressure effects on magnetic susceptibilities of FeSe and FeTe
compounds in the normal state. This comparison demonstrates a competing
interplay between superconductivity and magnetism in tellurium rich
FeSe$_{1-x}$Te$_x$ compounds
