A process for co-producing, from dialkyl maleates and hydrogen, dialkyl succinate and 1,4-butanediol, said process comprising the following steps: a) hydrogenating a stream of dialkyl maleate in a first stage of reaction over suitable catalyst to produce dialkyl succinate; b) further hydrogenating part of the dialkyl succinate produced in the first stage of reaction in a second stage of reaction, by using a different suitable catalyst, for producing mainly 1,4-butanediol, together with minor amounts of gamma-butyrolactone and tetrahydrofuran as co-products; the effluent is subject to cooling, phase separation and distillation to produce 1,4-butanediol, wherein, the first stage of reaction operates from 80 to 130 °C as inlet temperature, from 30 to 80 bar as pressure and with liquid hourly space velocity from 0.5 to 2.0 the second stage of reaction operates from 160 to 190 °C as inlet temperature, from 30 to 80 bar as pressure and with liquid hourly space velocity from 0.1 to 0.3 in both stages of reaction, the conditions as hydrogen/organic feed ratio, pressure and temperature are such to maintain the reactors in mixed liquid/vapor phase characterized in that: the effluent from the first stage of reaction is separated in a flash vessel to produce a liquid stream, rich in dialkyl succinate, and splitting this stream in three portions: i) a first part, corresponding to less than 50 %mol of total production, is further subject to low pressure phase separation, to separate the absorbed hydrogen, and to distillation to produce high purity dialkyl succinate; ii) a second part is sent to the second stage of reaction; iii) a recirculation liquid, which by a pump is cooled in a heat exchanger and sent back to the inlet of the first stage of reaction; the hydrogen/organic feed molar ratio is in the range from 15 to 30 in the first stage of reaction and from 30 to 60 in the second stage of reaction; and the dimethyl succinate, not converted in the second stage of reaction and separated in the distillation section in mixture with some amount of gamma-butyrolactone, is recycled to the second stage of reaction. a) hydrogenating a stream of dialkyl maleate in a first stage of reaction over suitable catalyst to produce dialkyl succinate; b) further hydrogenating part of the dialkyl succinate produced in the first stage of reaction in a second stage of reaction, by using a different suitable catalyst, for producing mainly 1,4-butanediol, together with minor amounts of gamma-butyrolactone and tetrahydrofuran as co-products; the effluent is subject to cooling, phase separation and distillation to produce 1,4-butanediol, wherein, the first stage of reaction operates from 80 to 130 °C as inlet temperature, from 30 to 80 bar as pressure and with liquid hourly space velocity from 0.5 to 2.0 the second stage of reaction operates from 160 to 190 °C as inlet temperature, from 30 to 80 bar as pressure and with liquid hourly space velocity from 0.1 to 0.3 in both stages of reaction, the conditions as hydrogen/organic feed ratio, pressure and temperature are such to maintain the reactors in mixed liquid/vapor phase characterized in that: the effluent from the first stage of reaction is separated in a flash vessel to produce a liquid stream, rich in dialkyl succinate, and splitting this stream in three portions: i) a first part, corresponding to less than 50 %mol of total production, is further subject to low pressure phase separation, to separate the absorbed hydrogen, and to distillation to produce high purity dialkyl succinate; ii) a second part is sent to the second stage of reaction; iii) a recirculation liquid, which by a pump is cooled in a heat exchanger and sent back to the inlet of the first stage of reaction; the hydrogen/organic feed molar ratio is in the range from 15 to 30 in the first stage of reaction and from 30 to 60 in the second stage of reaction; and the dimethyl succinate, not converted in the second stage of reaction and separated in the distillation section in mixture with some amount of gamma-butyrolactone, is recycled to the second stage of reaction. the effluent from the first stage of reaction is separated in a flash vessel to produce a liquid stream, rich in dialkyl succinate, and splitting this stream in three portions: i) a first part, corresponding to less than 50 %mol of total production, is further subject to low pressure phase separation, to separate the absorbed hydrogen, and to distillation to produce high purity dialkyl succinate; ii) a second part is sent to the second stage of reaction; iii) a recirculation liquid, which by a pump is cooled in a heat exchanger and sent back to the inlet of the first stage of reaction; i) a first part, corresponding to less than 50 %mol of total production, is further subject to low pressure phase separation, to separate the absorbed hydrogen, and to distillation to produce high purity dialkyl succinate; ii) a second part is sent to the second stage of reaction; iii) a recirculation liquid, which by a pump is cooled in a heat exchanger and sent back to the inlet of the first stage of reaction; the hydrogen/organic feed molar ratio is in the range from 15 to 30 in the first stage of reaction and from 30 to 60 in the second stage of reaction; and the dimethyl succinate, not converted in the second stage of reaction and separated in the distillation section in mixture with some amount of gamma-butyrolactone, is recycled to the second stage of reaction.