A model is presented of the unconventional local pair superconductivity in oxide superconductors. The most important predictions of this model associated with a peroxiton concept are applied to the superconducting transition in YBa 2(Cu 1 − x M x O 7 − y (M is a 3d transition metal). A formula for critical temperature as a function of substituent concentration x is obtained. The influence of oxygen deficiency on critical temperature is also explained.