An engine system comprises first and second electrical generators coupled to lower and higher pressure (LP, HP) shafts respectively of a gas turbine engine. A controller is arranged to receive a signal corresponding to a total electrical power demand P1 and to output control signals to the electrical generators in response thereto such that the first and second electrical generators output electrical powers (1−y)P1 and yP1 respectively when P1≤Pm1, where 0.5