The Cherenkov Telescope Array (CTA) is a future ground-based gamma-ray observatory that will provide unprecedented sensitivity and angular resolution for the detection of gamma rays with energies above a few tens of GeV. In comparison to existing instruments (like H.E.S.S., MAGIC, and VERITAS) the sensitivity will be improved by installing two extended arrays of telescopes in the northern and southern hemisphere, respectively. A large number of planned telescopes (>100 in total) motivates the application of predictive maintenance techniques to the individual telescopes. A constant and automatic condition monitoring of the mechanical telescope structure and of the drive system (motors, gears) is considered for this purpose. The condition monitoring system aims at detecting degradations well before critical errors occur; it should help to ensure long-term operation and to reduce the maintenance efforts of the observatory. We present approaches for the condition monitoring of the structure and the drive system of Medium-Sized Telescopes (MSTs), respectively. The overall concept has been developed and tested at the MST prototype for CTA in Berlin. The sensors used, the joint data acquisition system, possible analysis methods (like Operational Modal Analysis, OMA, and Experimental Modal Analysis, EMA) and first performance results are discussed.