The aim of our investigation was the determination of the epoch of the Leonid maximum for the return in 1966. We applied the same method, which has been used by Stoney and Downing (1899) for the investigation of motion of Leonids in 1899, e.g. method of variation of elements. Our attention has been concentrated on the motion of the position of the line of nodes, which is one of the important characteristics for the epoch of maximum activity of the shower. We started with the Adams elements – deduced from the splendid appearance of Leonids 1866, as did Stoney and Downing. We chose a 40-day interval for the integration step of perturbations as the most convenient, because all the positions of the great planets are tabulated with this interval in Washington tables (Eckert et al., 1951). Only the perturbations due to Jupiter, Saturn and Uranus during the years 1866–1966 have been considered as decisive for the motion of the Leonids' nodes. The computations for the epoch 1866–99 – divided into five parts – have been compared with those obtained by Stoney and Downing, with the results shown in Table 1.