The process of brazing heat exchangers made of stainless, creep-resisting and cryogenic steels 12Cr18Ni10Ti, VNS 16 and VNS 25 with a multilayer composite brazing alloy is developed. It is shown that the distribution of the elements of the brazing alloys Cr, Ni and Mn in the form of coatings eliminates the problems associated with wetting, spreading of the brazing alloy and clogging up of the cooling channels with a small cross section. The following parameters are determined: the chemical composition of the brazing alloy, the optimum thickness of the layers and the sequence of deposition of the layers of the smooth and finned surfaces. The experimental results show that the optimum brazing conditions (1150°C, 30 min+homogenizing annealing at 1000°C, 60 min) do not lead to any large decrease in the mechanical properties of the steels. The corrosion and mechanical properties of the brazed joints satisfy the service requirements. The strength of the brazed joints is equal to that of 12Cr18Ni10Ti steel. The process has been introduced in a number of important, large assembling systems. The mass of the components has been reduced by 30%.