We investigate a linear stability of the lower boundary of the hydrate stability zone (or the HSZ boundary) for deposits located in permafrost regions under the conditions of the geothermal gradient in the gravity field. We consider porous layers, one of which is saturated with methane and hydrate and another is saturated with methane and ice. Porous layers are of different permeabilities. The two types of background porous systems are studied: a discretely layered porous medium comprising two porous layers of constant different permeabilities, and a continuously layered porous medium consisting of a layer with permeability continuously varying with depth. It has been shown, that an essential difference in permeabilities of layers leads to the excitation of the "local convection" within the lower more permeable gas-ice layer, whereas at close values of layer permeabilities the instability occurs in the form of a "large-scale convection" covering both the gas-ice and gas-hydrate layers. (C) 2016 Elsevier Ltd. All rights reserved.