An image-pickup system is disclosed which is capable of performing highly accurate back focus adjustment for each combination of an image-pickup apparatus and a lens apparatus. The system includes a first memory provided in the image-pickup apparatus and stores first identification information unique to a combination of the image-pickup apparatus and a certain lens apparatus, a second memory provided in the lens apparatus and stores second identification information unique to a combination of the lens apparatus and a certain image-pickup apparatus. A comparator compares the first identification information with the second identification information. The generator generates, when the comparison results that the first identification information does not match the second identification information, identification information unique to the combination of the image-pickup apparatus and the lens apparatus. The controller causes the first memory and the second memory to store the identification information generated by the generator.