Disclosed is apparatus for breathing with hypoxic gaseous mixtures. The apparatus comprises of: a supporting frame; a respiratory reservoir equipped with an inspiration valve, a first sensor of oxygen content and an absorber of CO2 and H2O; a controllable compressor connected via puffing valve to the respiratory reservoir; and a chamber for sampling and accumulation of aliquots of expired gaseous mixtures equipped with a second sensor of oxygen content, controllable adjusting valve and controllable ejector. The apparatus also includes means for attachment to a user, such as a mask; an inspiration line comprising controllable centre valve and first inspiratory rate flowmeter; a tee fitting; main expiration line that is equipped with first air blower and connects said attachment with said reservoir; additional expiration line that is equipped with second flowmeter measuring volume of sampling aliquots and second air blower and connects said attachment with said chamber; and a supplementary sensor complex and program control unit. This apparatus provides for the estimation of minute oxygen consumption and, accordingly, efficiency of regulation of breathing with hypoxic gaseous mixtures.