The possible influence of static stress transfers on the moderate and small earthquake activity within the Pamir Hindu Kush seismic zone, in the brittle contact zone where the Indian and Eurasian lithospheric plates interact, is investigated. We consider 129 small and moderate earthquakes that occurred in this region between 1960 and 2002. We assume that these earthquakes were caused mainly by normal frictional sliding processes and that, to a first order of approximation, the rates of stress/strain accumulation in the elastico-viscous upper mantle rocks here are constant in time. We compute Coulomb failure stresses that were transferred from these earthquakes to other prestressed earthquake faults of the region. The computed positive/negative static stress transfers are often cumulatively large enough to suggest significant promotion/inhibition of future small and moderate earthquake activity here. Our analysis suggests that, in the region of investigation, transferred static stresses significantly modulate the ambient stress field, influencing the moderate and small earthquake activity here in an important way.