We have shown that in CdTe/Cd1-xMgxTe heterostructures revealing parallel t
ransport, hydrostatic pressure induces a decrease in both 2D conduction in
the quantum well and in low mobility parallel channel. This behaviour, cont
rary to III-V heterostructures, is due to persistent decrease of the mobili
ty. For samples having thick buffer layer the contribution of the parallel
conduction is practically eliminated at high pressure with 2D conduction re
maining dominant, while for samples with thin buffer layer the situation wi
th pure 2D conduction is not achieved.