Process for the initiation of a process for the production of kerosene and diesel fuel from hydrocarbon compounds produced by the Fischer-Tropsch synthesis, in which the following stages are carried out: a) a catalytic Fischer-Tropsch synthesis reaction is carried out with a synthesis gas in order to produce a heavy hydrocarbon fraction and a light hydrocarbon fraction, b) a reduction of a hydrotreating catalyst comprising molybdenum and nickel and a support comprising alumina is carried out by bringing into contact with a hydrogen-comprising gas, then stage c) is carried out, c) the heavy hydrocarbon fraction is brought into contact with the hydrotreating catalyst, d) during stage c), the temperature (TEMP) of the hydrotreating catalyst is increased up to a temperature of between 260°C and 360°C, then stage e) is carried out, e) a mixture comprising the heavy hydrocarbon fraction and the light hydrocarbon fraction is brought into contact with the hydrotreating catalyst, f) after stage e), the mixture comprising the heavy hydrocarbon fraction and the light hydrocarbon fraction continues to be brought into contact with the hydrotreating catalyst under the following operating conditions: - a temperature of between 100 and 450°C, - a total pressure of between 0.5 and 15 MPa, - a hydrogen flow rate such that the ratio by volume of hydrogen with respect to the hydrocarbon feedstock is between 100 and 3000 Sl/l/h, - an hourly space velocity of between 0.1 and 10 h -1, then the effluent from stage f) is brought into contact in the presence of hydrogen and of a hydrocracking and hydroisomerization catalyst comprising platinum and a support chosen from a silica/alumina and a zeolite under the following operating conditions: - a temperature of between 200 and 450°C, - a total pressure of between 0.2 and 15 MPa, - a hydrogen flow rate such that the ratio by volume of hydrogen with respect to the hydrocarbon feedstock is between 100 and 2000 Sl/l/h, - an hourly space velocity of between 0.1 and 10 h -1. a) a catalytic Fischer-Tropsch synthesis reaction is carried out with a synthesis gas in order to produce a heavy hydrocarbon fraction and a light hydrocarbon fraction, b) a reduction of a hydrotreating catalyst comprising molybdenum and nickel and a support comprising alumina is carried out by bringing into contact with a hydrogen-comprising gas, then stage c) is carried out, c) the heavy hydrocarbon fraction is brought into contact with the hydrotreating catalyst, d) during stage c), the temperature (TEMP) of the hydrotreating catalyst is increased up to a temperature of between 260°C and 360°C, then stage e) is carried out, e) a mixture comprising the heavy hydrocarbon fraction and the light hydrocarbon fraction is brought into contact with the hydrotreating catalyst, f) after stage e), the mixture comprising the heavy hydrocarbon fraction and the light hydrocarbon fraction continues to be brought into contact with the hydrotreating catalyst under the following operating conditions: - a temperature of between 100 and 450°C, - a total pressure of between 0.5 and 15 MPa, - a hydrogen flow rate such that the ratio by volume of hydrogen with respect to the hydrocarbon feedstock is between 100 and 3000 Sl/l/h, - an hourly space velocity of between 0.1 and 10 h -1, then the effluent from stage f) is brought into contact in the presence of hydrogen and of a hydrocracking and hydroisomerization catalyst comprising platinum and a support chosen from a silica/alumina and a zeolite under the following operating conditions: - a temperature of between 200 and 450°C, - a total pressure of between 0.2 and 15 MPa, - a hydrogen flow rate such that the ratio by volume of hydrogen with respect to the hydrocarbon feedstock is between 100 and 2000 Sl/l/h, - an hourly space velocity of between 0.1 and 10 h -1. - a temperature of between 100 and 450°C, - a total pressure of between 0.5 and 15 MPa, - a hydrogen flow rate such that the ratio by volume of hydrogen with respect to the hydrocarbon feedstock is between 100 and 3000 Sl/l/h, - an hourly space velocity of between 0.1 and 10 h -1, - a temperature of between 200 and 450°C, - a total pressure of between 0.2 and 15 MPa, - a hydrogen flow rate such that the ratio by volume of hydrogen with respect to the hydrocarbon feedstock is between 100 and 2000 Sl/l/h, - an hourly space velocity of between 0.1 and 10 h -1.