The invention concerns a process for producing at least one compound selected from 2-, 3-, 4-, 5- and 6-phenylalkanes by alkylating benzene using at least one olefin containing at least 9 carbon atoms per molecule, in the presence of a catalyst comprising at least one zeolite with structure type EUO, at least partially in its acid form and at least one matrix, said zeolite comprising silicon and at least one element T selected from the group formed by aluminium, iron, gallium and boron (preferably aluminium and boron), with an Si/T atomic ratio of more than 5; said process being carried out at a temperature in the range 30° C. to 400° C., a pressure in the range 0.1 to 10 MPa, with an hourly space velocity of 0.50 to 200 h−1, and a benzene/olefins mole ratio in the range 1:1 to 50:1.