We compiled a list of 240 eclipsing binaries with light-time effect (LITE). Under the assumption that there are additional components in these stars, some values for multiple systems are given. Distributions for the number of close binary systems (CBS) showing LITE and with out this effect are constructed and it is shown that the observed excess of short-period (less than 0.3 day) CBS with LITE really exists. The distribution for the eccentricities of long-period orbits (LPO) is parabolic with a weak maximum at e=0.28. The ratio of LPO period to CBS period cannot be considered as a random one. A relationship between these values and LPO’s periods is revealed. The distributions for the periods and semi-major axes of LPO show maxima at P₃=32 yrs and a=16 AU, respectively. The second distribution can be described through the Gaussian function. Some 85% of the third components have masses which are half as much as the total masses of the CBS. Except for one CBS (RR Lyn), all the multiple systems from our list are dynamically stable configurations. We consider the possibility to detect tertiary companions from speckle-interferometric observations, from the analysis of proper motions of CBS, from the search for additional light contribution in light curves and from changes in radial velocities of centres of mass of CBS. Some other causes for LITE are considered, namely, the mass exchange in CBS and the influence of magnetic fields of components. Some difficulties in the explanation of LITE through magnetic fields of components are noted. Some perspective ways to reveal tertiary components in CBS with LITE are proposed.