There are provided an endoscope system and a method of operating the endoscope system that can store and display images, which are obtained using a plurality of kinds of illumination light and have a small shake amount, as static images.An image processing unit (60) includes a shake amount calculation section (72) and a static image-storage control section (74), and the shake amount calculation section (72) includes a shake amount-calculation processing section (78) and an algorithm switching section (80). The algorithm switching section (80) applies an algorithm varying for each image, and selects images of which the shake amounts calculated by the shake amount-calculation processing section (78) are small. A first image and a second image, which are selected as the images of which the shake amounts are small, are stored in a static image-storage unit (76). A display control unit (62) displays static images for storage.