An accessory apparatus detachably attachable to an image pickup apparatus and capable of communicating with the image pickup apparatus by using a plurality of communication methods, the accessory apparatus comprising: accessory side setting means for setting a communication method to be used for communication with the image pickup apparatus; and power control means for, upon reception of a signal transmitted from the image pickup apparatus, switching between a first power state where communication with the image pickup apparatus is possible and a second power state which provides smaller power consumption than the first power state, characterized in that when attached to the image pickup apparatus, the accessory apparatus is configured to perform initial communication for transmitting, to the image pickup apparatus, information about a communication method supported by the accessory apparatus, the accessory side setting means is capable of switching a communication setting of the accessory apparatus between a first setting corresponding to a first communication method that is the communication method used in the initial communication and a second setting corresponding to a second communication method different from the first communication method, in a case where the communication setting of the accessory apparatus is the first setting, the power control means is configured to perform switching from the first power state to the second power state upon reception of the signal transmitted from the image pickup apparatus, and in a case where the communication setting of the accessory apparatus is the second setting, the power control means is configured to not perform switching from the first power state to the second power state. accessory side setting means for setting a communication method to be used for communication with the image pickup apparatus; and power control means for, upon reception of a signal transmitted from the image pickup apparatus, switching between a first power state where communication with the image pickup apparatus is possible and a second power state which provides smaller power consumption than the first power state, characterized in that when attached to the image pickup apparatus, the accessory apparatus is configured to perform initial communication for transmitting, to the image pickup apparatus, information about a communication method supported by the accessory apparatus, the accessory side setting means is capable of switching a communication setting of the accessory apparatus between a first setting corresponding to a first communication method that is the communication method used in the initial communication and a second setting corresponding to a second communication method different from the first communication method, in a case where the communication setting of the accessory apparatus is the first setting, the power control means is configured to perform switching from the first power state to the second power state upon reception of the signal transmitted from the image pickup apparatus, and in a case where the communication setting of the accessory apparatus is the second setting, the power control means is configured to not perform switching from the first power state to the second power state.