Аннотация:CI Cam (XTE J0421+560) is an X-ray transient and a binary system with the optical companion, which shows the B[e] phenomenon. Its strong all-wavelength outburst occured in 1998 April. The system consists of a B4 III-V star and a possible white dwarf on an eccentric (e = 0.62) orbit with the period of 19.407 day (ATel #416; Astronomy Reports, 2006, V.50, 664). We analysed seventeen echelle spectra (resolution FWHM=0.08-0.21A) taken with Russian 6-m telescope BTA (LYNX and NES spectrographs), CFHT (ESPaDOnS spectrograph), and McDonald 2.1-m (Sandiford spectrograph) and 2.7-m (cs2 spectrograph) telescopes. The spectroscopic observations were performed between 1999 January 27 and 2006 December 25. The centroid velocities of the following emission lines were measured: FeII (5 lines), [N II] 5754.59A (NIST Database), H_alpha, H_beta, HeI (5 lines), and [O III]5006.843A. FeII and [N II] lines that form in the cool equatorial disk wind of B[e] star have stable sharp-edge profiles. The velocity dispersion measured in individual spectra using the set of five FeII lines varies between 0.4 and 1.0 km/s. To check the accuracy of the stellar velocities and heliocentric corrections, we also measured centroid velocities of narrow telluric [O I] emission line and two components of the interstellar NaI D_2,D_1 absorption lines. All the FeII lines and the [N II] line in our spectra show a linear shift with time. The line profiles shift as a whole, and their edges move synchronously. These shifts do not correlate with the phase of the 19.41 day period. The acceleration is equal to -1.70 +/-0.06 km/s per year in the FeII lines, and -1.60 +/-0.06 km/s per year in the [N II] line. The Balmer and HeI lines show a similar velocity shift tendency, which is measured with a lower accuracy due to an additional short-term (days) variability of the lines' shape and velocity. The shift of lines may be evidence for the third companion in the system of CI Cam. The FeII line velocity changed between -42.3 and -55.7 km/s during the last 7.9 years, and this shift is seen around the gamma-velocity of -51 km/s of the 19.407-day HeII-line velocity curve (this period is confirmed with our high-resolution spectra). This indicates that the B4 star and its line forming region along with its compact companion is passing now the exterior conjunction of its orbit around invisible companion. The orbital period of the latter should be over 40 years. Therefore the system of CI Cam is hierarchic. But such a shift in the [NII] forbidden line is surprising. This line was the only one which has not strengthened in the April 1998 outburst. Its intensity began to rise only 20 days after the X-ray peak and reached maximum with the time delay of 210 +/-20 days. The radius of its forming region may be as large as 150-200 AU. It is hard to imagine a regular acceleration of such a large nebula.