The lithium problem in Ap-CP stars has been, for a long time, a subject of debate. Individual characteristics of CP stars, such as high abundance of the rare-earth elements presence of magnetic fields, complicate structure of the surface distribution of chemical elements, rapid oscillations of some CP-stars, make the detection of the lithium lines and the determination of the lithium abundance, a difficult task. During the International Meeting in Slovakia in 1996, the lithium problem in Ap-CP stars was discussed. The results of the Li study carried out in CrAO Polosukhina (1973–1976), the works of Hack & Faraggiana (1963), Wallerstein & Hack (1964), Faraggiana et al. (1992–1996) formed the basis of the International project ‘Lithium in the cool CP-stars with magnetic fields’. The main goal of the project was, using systematical observations of Ap-CP stars with phase rotation in the spectral regions of the resonance doublet Li I 6708 Å and subordinate 6104 Å lithium lines with different telescopes, to create a database, which will permit to explain the physical origin of anomalous Li abundance in the atmospheres of these stars.