We have used neutron reflection measurements to determine the structure of monolayers of the cationic gemini surfactants (alpha,omega)-bis(N-alkyl dimethylammonium) alkane bromides (CnCmCn) adsorbed at the air/water interface at the critical micelle concentration and at 1/10 of this concentration. The compounds studied all had hydrophobic chains of 12 carbons (n = 12), and the spacers were m = 3, 4, 6, 12, and xylyl. Partial deuteration was used to distinguish the spacer and chain groups. In all of the compounds except that with m = 12, the spacer remains close to the headgroups and partially immersed in water. The C-12 spacer, however, is part of the strongly hydrophobic region of the layer. The most surprising feature of the layers is that a low-concentration single layer of surfactant forms below the main layer at an approximate distance of 15-20 Angstrom from the center of the headgroup, distribution. The area per molecule in this secondary layer varies between about 800 and 2500 Angstrom and does not seem to show any particular concentration dependence. More detailed fitting leads to the tentative conclusion that the molecules in the secondary layer are oriented with their charged groups pointing away from the aqueous subphase and toward the charged groups in the main monolayer. It is possible that this sublayer is a manifestation of the tendency of the geminis to undergo premicellar aggregation that has been proposed independently by other researchers.