By means of the Gauss-Halphen-Goryachev method secular orbital variations have been studied for a period of 4000 yr (from −50 to +3950). The method has been applied to the periodic comets Halley, Brorsen-Metcalf, Pons-Brooks, Westphal, Olbers, Neujmin 1, and Encke. Investigations have demonstrated that the use of the method for most comets is not expedient as it does not allow for the possibility of approaches to the major planets and thus does not reflect the real evolution of the cometary orbits. Application of the method over the interval of 2000 years back from the epoch 1950.0 for the planets 279 Thule, 1162 Larissa, 1180 Rita, and 1202 Marina, as well as from the epoch 1850.0 for 1 Ceres has given adequate results and has displayed the stability of these orbits. Study of the secular perturbations on the Leonids over the interval of 4000 yr has confirmed the stability of that meteor stream. By means of the same method 14 minor meteor streams were investigated, and their orbits also proved to be stable. The availability of the various systems of osculating elements has permitted us to estimate for the first time the possibility of the encounter of those streams with the Earth over a 4000-yr period. For further details see Galibina (1970a, 1970b, 1971).