The present invention relates to control circuits and methods for a flyback converter and AC-DC power converters thereof. In one embodiment, a control circuit can include: (i) a turn-on signal generating circuit that is configured, in each switching cycle, to receive a drain-source voltage of a power switch of the flyback converter, and to activate a turn-on signal to turn on the power switch when the drain-source voltage reaches a valley value; (ii) a turn-off signal generating circuit that is configured, in each switching cycle, to activate a turn-off signal to turn off the power switch based on a power switch feedback error signal after a power switch conducting time interval has elapsed; and (iii) where input current and voltages of the flyback converter can be maintained as substantially in phase, and an output electrical signal of the flyback converter can be maintained as substantially constant.