NOVELTY - The device (D) has a control unit (MC) arranged to operate a converter (C1) at full power in a phase so as to recharge a battery (B1) until stored energy threshold is obtained to allow an operation of a hybrid vehicle (V) in a non rechargeable hybrid mode and in another phase so as to recharge the battery until another stored energy threshold is obtained to allow recovery of deceleration energy of the vehicle. The control unit operates the converter and another converter (C2) at maximum power in third phase so as to terminate recharging of the battery and another battery (B2) of the vehicle.    USE - Control device for controlling recharging of batteries e.g. multi-cellular rechargeable batteries such as Lithium-ion, lead and nickel-maleic hydrazide batteries, of a hybrid vehicle (claimed) on an external power supply network i.e. grid.    ADVANTAGE - The device assures starting of the heat engine, utilization of the hybrid vehicle and operating the vehicle in non-rechargeable hybrid mode at the starting of running so as to decrease fuel consumption of the vehicle. The device immediately recovers the energy of the majority of decelerations and decreasing fuel consumption by increasing electric autonomy. The device enables optimizing the electrical energy consumed on the external electrical supply network, ageing of the batteries and optimizing the thermal management of the vehicle.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for the following:    (1) a logic controller for a hybrid vehicle    (2) a method for controlling recharging of batteries of a hybrid vehicle.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic block diagram of a hybrid vehicle comprising rechargeable batteries on a grid, battery charger, converters, electric equipments and a logic controller comprising a device for controlling recharging of batteries of a hybrid vehicle.    Rechargeable batteries (B1, B2)    Converters (C1, C2)    Control device (D)    Control unit (MC)    Heat engine (M1)    Hybrid vehicle (V)