We study the relationship between coronal mass ejections (CMEs) and the increase in the intensity of energetic (Ee>0.3 MeV) electrons in interplanetary space (IS). For analysis we used the data on the CME observations from P78-1 satellite and the events in solar energetic particles (SEP) from the Helios 1, 2, ISEE 3, and Venera 13, 14 spacecrafts in the period from 1979 to 1983. Nine SEP events were observed simultaneously at different points of the IS. We found that the time Tmn from the beginning of the solar perturbation to the maximum of energetic electron intensity Jmn, as well as the intensity Jmn itself, are statistically related to the CME velocity, and this relation is characterized by the correlation factor R ∼0.6 to 0.9 for different samples of events. The correlation factors Jmn with the amplitude of thermal X-ray (Xt) radiation of flares do not exceed ∼0.5 to 0.6 for the same samples. The results of the statistical approach indicate acceleration of energetic electrons at coronal shock waves initiated by CMEs.