Process for continuous industrial preparation of alkanesulfonic acid of formula C n H 2n+1 SO 3 H starting from the alkane of formula C n H 2n+2, where n represents an integer between 1 and 20 inclusive, preferably between 1 and 12 inclusive, more preferably between 1 and 6 inclusive, and for example equal to 1, 2 or 3, said process comprising at least the following steps: a) charging a reactor with alkanesulfonic acid C n H 2n+1 SO 3 H, where n is as defined above, b) heating said alkanesulfonic acid to a temperature of between 25°C and 120°C, preferably of between 25°C and 100°C, more preferably of between 25°C and 70°C, c) introducing an amount of sulfur trioxide such that the (alkanesulfonic acid)/(sulfur trioxide) molar ratio is between 70/30 and 95/5, d) introducing the alkane under a pressure of between 4 MPa and 15 MPa, preferably of between 5 MPa and 12 MPa, d) introducing a free-radical initiator, e) carrying out the reaction in a continuous manner, by simultaneous, sequential or alternating operation of the following three substeps e1), e2) and e3): e1) adding sulfur trioxide so as to maintain the initial (alkanesulfonic acid)/(sulfur trioxide) molar ratio defined in step c), e2) adding the alkane so as to maintain an (alkane)/(sulfur trioxide) molar ratio between 4/1 and 2/1, preferably of between 3.5/1 and 2.5/1, typically so as to maintain an (alkane)/(sulfur trioxide) molar ratio equal to about 3, and e3) continuously withdrawing the alkanesulfonic acid of formula C n H 2n+1 SO 3 H, and f) recovering the alkanesulfonic acid of formula C n H 2n+1 SO 3 H after optional separation of unreacted reactants and of possible undesired by-products. a) charging a reactor with alkanesulfonic acid C n H 2n+1 SO 3 H, where n is as defined above, b) heating said alkanesulfonic acid to a temperature of between 25°C and 120°C, preferably of between 25°C and 100°C, more preferably of between 25°C and 70°C, c) introducing an amount of sulfur trioxide such that the (alkanesulfonic acid)/(sulfur trioxide) molar ratio is between 70/30 and 95/5, d) introducing the alkane under a pressure of between 4 MPa and 15 MPa, preferably of between 5 MPa and 12 MPa, d) introducing a free-radical initiator, e) carrying out the reaction in a continuous manner, by simultaneous, sequential or alternating operation of the following three substeps e1), e2) and e3): e1) adding sulfur trioxide so as to maintain the initial (alkanesulfonic acid)/(sulfur trioxide) molar ratio defined in step c), e2) adding the alkane so as to maintain an (alkane)/(sulfur trioxide) molar ratio between 4/1 and 2/1, preferably of between 3.5/1 and 2.5/1, typically so as to maintain an (alkane)/(sulfur trioxide) molar ratio equal to about 3, and e3) continuously withdrawing the alkanesulfonic acid of formula C n H 2n+1 SO 3 H, and e1) adding sulfur trioxide so as to maintain the initial (alkanesulfonic acid)/(sulfur trioxide) molar ratio defined in step c), e2) adding the alkane so as to maintain an (alkane)/(sulfur trioxide) molar ratio between 4/1 and 2/1, preferably of between 3.5/1 and 2.5/1, typically so as to maintain an (alkane)/(sulfur trioxide) molar ratio equal to about 3, and e3) continuously withdrawing the alkanesulfonic acid of formula C n H 2n+1 SO 3 H, and f) recovering the alkanesulfonic acid of formula C n H 2n+1 SO 3 H after optional separation of unreacted reactants and of possible undesired by-products.