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In recent years, much has been studied on the colonoscope because it is a very important tool for diagnosing colon cancer which is the second leading cause of cancer in the developed countries. During the course of colonoscopy, the colonoscope need to be inserted to the tortuous colon of patients. This is a procedure often painful for the patient and complex for the surgeon. In order to solve this problem, a new flexible actuator of a colonoscope capable of avoiding the injury to the patients has been developed for autonomous colonoscope in our lab. In this paper we mainly deal with the modeling and parameter identification of our flexible actuator in order to design a controller that can automatically detect the contact between the surgical instruments and the intestine. First a mathematical model of the actuator was deduced and linearised from previous research, then a direct identification approach was studied for the continuous-time system, using continuous-time ARX (CARX) model and the Levenberg Marquardt (L-M) algorithm. Finally, the experiment setup and the identification of the parameters of the actuator are described and the results are compared with the data obtained from classical frequency response method. Experimentation has proved the continuous-time method to be very effective for our system identification.