An option is a short-term skill consisting of a control policy for a specified region of the state space, and a termination condition recognizing leaving that region. In prior work, we proposed an algorithm called Deep Discovery of Options (DDO) to discover options to accelerate reinforcement learning in Atari games. This paper studies an extension to robot imitation learning, called Discovery of Deep Continuous Options (DDCO), where low-level continuous control skills parametrized by deep neural networks are learned from demonstrations. We extend DDO with: (1) a hybrid categorical–continuous distribution model to parametrize high-level policies that can invoke discrete options as well continuous control actions, and (2) a cross-validation method that relaxes DDO’s requirement that users specify the number of options to be discovered. We evaluate DDCO in simulation of a 3-link robot in the vertical plane pushing a block with friction and gravity, and in two physical experiments on the da Vinci surgical robot, needle insertion where a needle is grasped and inserted into a silicone tissue phantom, and needle bin picking where needles and pins are grasped from a pile and categorized into bins. In the 3-link arm simulation, results suggest that DDCO can take 3x fewer demonstrations to achieve the same reward compared to a baseline imitation learning approach. In the needle insertion task, DDCO was successful 8/10 times compared to the next most accurate imitation learning baseline 6/10. In the surgical bin picking task, the learned policy successfully grasps a single object in 66 out of 99 attempted grasps, and in all but one case successfully recovered from failed grasps by retrying a second time.