In the evolution of many organisms, periods of very slow genome reorganization (=chromosomal conservatism) are interrupted by bursts of numerous chromosomal changes (=chromosomal megaevolution). However, the patterns, mechanisms, and consequences of conservative and rapid chromosomal evolution are still poorly understood and widely discussed. Here we show that in blue butterflies (Lepidoptera: Lycaenidae), the periods of chromosome number conservatism are characterized by the real stability of most autosomes and the highly dynamic evolution of the sex chromosome Z, which, due to autosome-sex chromosome fusions and fissions, is carried out according to the cycle Z=>NeoZ1=>Z=>NeoZ2=> Z=>NeoZ3. These fusions and fissions result in a fluctuation of chromosomal number around the ancestral value, a phenomenon previously observed (but not explained) in numerous groups of Lepidoptera. In the phase of chromosomal megaevolution, the explosive increase in the chromosome number occurs mainly due to simple chromosomal fissions, in some cases complicated by autosomal translocations. Interestingly, these translocations are not random and found to occur only between fragmented chromosomes originated from the same primary linkage group. We also found that the Z chromosomes of two closely related Lysandra species are differentiated by a large inversion. We argue that the special role of sex chromosomes in speciation can be reinforced via sex chromosome - autosome fusion. The cycles of fusions and fissions of sex chromosomes with autosomes, such as those found in the blue butterflies, indicate that the species divergence driven by neo-Z chromosome formation is widely distributed in Lepidoptera.