•Critical points in charge density of Bi and Sb chalcogenides are found.•Premises for charge density fluctuations in Bi and Sb chalcogenides are revealed.•Charge density fluctuations are proposed to be the origin of anomalous properties.•Existence of local magnetic fields in Sb2S3 is found. Electron band structure calculations and analysis of critical points parameters in the electron density distribution in Bi2Te3, Bi2Se3, Bi2S3, α-Bi2O3, Sb2Te3, Sb2Se3 and Sb2S3 at ambient and high pressures were performed to determine interrelations between the crystal structure, unusual physical (including magnetic and superconducting) properties and peculiarities in the electron density distribution. The programming code WIEN2k was used for band structure calculations. The previously found correlation between the superconducting transition temperature Tc and the electron density Laplacian value in the bond critical point with the highest electron density was confirmed by the calculations made for crystal structures under high pressure. The revealed parameters of bond critical points indicate the significant role of charge density fluctuations in the compounds studied. The 121, 123Sb NQR spin echo envelopes assigned to the ν1 transition (Δm = 1/2–3/2) were measured for the two crystallographic positions of Sb atoms in the Sb2S3 structure. Unexpectedly deep oscillations of NQR spin echo envelopes were observed in very small (1–3 Oe) external magnetic fields, evidencing for the existence of local magnetic fields in Sb2S3 similar to those earlier observed in bismuth oxide compounds.