For researchers, the problem of interpreting the origin nature of NQR spectra multiplicity is always one of the main experimental tasks.For the purpose of interpreting the nature of the occurrence of NQR spectra multiplicity in the layered crystal InSe, the spectra of NQR 113,115 In for four spin transitions, the average values of which are only approximately satisfied the ratio ν1: ν2: ν3: ν4 =1: 2:3:4 were studied. In the studied NQR spectra, two multiplet groups, confirming the presence of polytypic structure in crystals are clearly observed. The feature of multiplet groups is the presence of fine structure with the splitting constant, which is clearly observed for the three higher transitions and constitutes10 ± 0,5 kHz. The quantitative similarity of the spectra 113,115 In in InSe reflects that the corresponding splitting occurs almost entirely due to the interaction of nuclei In. It is established that for higher transitions deviation is observed. It is shown that, in multiplet groups for higher-order transitions, multiplet groups of lines are observed that, in our opinion, is connected with the presence hexadecapole interaction with the electric field gradient of crystal.This interaction is caused not only by p-, but also d-, f- electrons in layered crystal with highly distorted configuration of the charge distribution in the vicinity of indium nuclei. In addition, as a result of exciting the electrons d- or f- of the indium atom shell by coordinating interactions, the additional contribution of hexadepole moment in the form of additional lines in the multiplet spectra of NQR may occur.