The invention relates to a process for assembling a first element that includes at least one first wafer, substrate or at least one chip, and a second element of at least one second wafer or substrate, involving the formation of a surface layer, known as a bonding layer, on each substrate, at least one of the bonding layers being formed at a temperature less than or equal to 300° C.; conducting a first annealing, known as degassing annealing, of the bonding layers, before assembly, at least partly at a temperature at least equal to the subsequent bonding interface strengthening temperature but below 450° C.; forming an assembling of the substrates by bringing into contact the exposed surfaces of the bonding layers, and conducting an annealing of the assembled structure at a bonding interface strengthening temperature below 450° C.