A new microscopic analysis of the central-peak phenomena caused by thermal fluctuations near the order-disorder phase transitions is given. This is based on new results obtained recently in the dynamics of the disordered phase of ferroelectrics in the framework of the three-dimensional spin- 1/2 Ising model in a transverse field and performed by the Green function method. A microscopic description for all the parameters of a phenomenological model adopted in the central-peak problem is given. In particular, the central-peak observation conditions are formulated. A new critical behaviour of the central relaxation-type mode, namely gamma _c approximately (T-T_c)^5/4 is found. A minimum of the soft mode is predicted above the critical temperature T_c.