Method for hydroconversion of heavy oils in a single reaction stage comprising the following steps: a) feeding, at the base, at least one reactor of the type with dispersed catalyst or of the type with expanded catalyst bed with: • heavy oil comprising at least 10% by weight of hydrocarbons having, at atmospheric pressure, a boiling point higher than 540 °C; • a first gas including hydrogen; • a hydroconversion catalyst, generating: • at least at a lower part of said reactor, reaction liquid traversed by said first gas, and • at least at an upper part of said reactor placed above said reaction liquid traversed by said first gas, a biphasic foam including at least one liquid phase and one gaseous phase, said biphasic foam originating a biphasic effluent upon exiting from the head of said reactor, b) drawing said biphasic effluent from said upper part of the reactor and separating the liquid phase from the gaseous phase of said biphasic effluent; c) subjecting said liquid phase to flash-atmospheric distillation; d) subjecting to concentration, via vacuum distillation, a first residue of said flash-atmospheric distillation; e) introducing, at the base, in said reactor a second residue of said concentration via vacuum distillation, the hydroconversion method being characterized in that, in step a), a second gas is introduced into said upper part of the reactor, at a zone of said reactor containing said biphasic foam, in addition: • said reactor operating at a temperature comprised between 330 °C and 430 °C, and at a pressure comprised between 10 MPa and 30 MPa; • said second gas being introduced into said upper part of the reactor in step a), and said second residue being introduced into said reactor in step e), with respective flow rates such that the density of said biphasic foam measured following the introduction of said second gas in said upper part of the reactor, is comprised between 100 kg/m 3 and 500 kg/m 3; • in step a), said second gas being introduced into said upper part of the reactor at a superficial velocity comprised between 0.1 cm/s and 50 cm/s; • in step b), said biphasic effluent being originated with a superficial velocity of the gas equal to at least 10 times the liquid flow velocity; • in step a), said second gas being introduced into said upper part of the reactor at a temperature such that the temperature of said biphasic foam is comprised between 330 °C and 430 °C; • in step e), said second residue being introduced into said reactor at a unit flow rate at least equal to 0.5 x Vs x H, where Vs is the space velocity with which, in step a), said heavy oil is introduced into said reactor and H is the height of said reactor. a) feeding, at the base, at least one reactor of the type with dispersed catalyst or of the type with expanded catalyst bed with: • heavy oil comprising at least 10% by weight of hydrocarbons having, at atmospheric pressure, a boiling point higher than 540 °C; • a first gas including hydrogen; • a hydroconversion catalyst, generating: • at least at a lower part of said reactor, reaction liquid traversed by said first gas, and • at least at an upper part of said reactor placed above said reaction liquid traversed by said first gas, a biphasic foam including at least one liquid phase and one gaseous phase, said biphasic foam originating a biphasic effluent upon exiting from the head of said reactor, • heavy oil comprising at least 10% by weight of hydrocarbons having, at atmospheric pressure, a boiling point higher than 540 °C; • a first gas including hydrogen; • a hydroconversion catalyst, • at least at a lower part of said reactor, reaction liquid traversed by said first gas, and • at least at an upper part of said reactor placed above said reaction liquid traversed by said first gas, a biphasic foam including at least one liquid phase and one gaseous phase, said biphasic foam originating a biphasic effluent upon exiting from the head of said reactor, b) drawing said biphasic effluent from said upper part of the reactor and separating the liquid phase from the gaseous phase of said biphasic effluent; c) subjecting said liquid phase to flash-atmospheric distillation; d) subjecting to concentration, via vacuum distillation, a first residue of said flash-atmospheric distillation; e) introducing, at the base, in said reactor a second residue of said concentration via vacuum distillation, • said reactor operating at a temperature comprised between 330 °C and 430 °C, and at a pressure comprised between 10 MPa and 30 MPa; • said second gas being introduced into said upper part of the reactor in step a), and said second residue being introduced into said reactor in step e), with respective flow rates such that the density of said biphasic foam measured following the introduction of said second gas in said upper part of the reactor, is comprised between 100 kg/m 3 and 500 kg/m 3; • in step a), said second gas being introduced into said upper part of the reactor at a superficial velocity comprised between 0.1 cm/s and 50 cm/s; • in step b), said biphasic effluent being originated with a superficial velocity of the gas equal to at least 10 times the liquid flow velocity; • in step a), said second gas being introduced into said upper part of the reactor at a temperature such that the temperature of said biphasic foam is comprised between 330 °C and 430 °C; • in step e), said second residue being introduced into said reactor at a unit flow rate at least equal to 0.5 x Vs x H, where Vs is the space velocity with which, in step a), said heavy oil is introduced into said reactor and H is the height of said reactor.