An X-ray study of Bi1-xSbx alloys in the concentration range x = 0 – 0.1 was carried out. It was established that up to an Sb concentration x ~ 0.02, the unit cell parameters (a, c) decrease linearly with increasing concentration, and the diffraction linewidth increases. In the concentration interval of x = 0.025 – 0.1 the a(x) and c(x) curves noticeably deviate from the Vegard straight line, with maximum deviations corresponding to the compositions at which the transition to a gapless state and the energy band inversion occurs (x = 0.03 – 0.035) and the semimetal-semiconductor transition (x = 0.06 – 0.07) takes place. In the indicated concentration regions, and also in the interval x = 0.005 – 0.01, a decrease in the X-ray diffraction line width is observed. It is suggested that the structural instability occurring in these special concentration ranges in Bi1-xSbx solid solutions is connected with changes in the electron spectrum under the percolation transition, the transition into a gapless state and band inversion and under a semimetal – semiconductor transition