The instrumental line background of the Compton telescope COMPTEL onboard the Compton Gamma-Ray Observatory is due to the activation and/or decay of many isotopes. The major components of this background can be attributed to eight individual isotopes, namely 2D, 22Na, 24Na, 28Al, 40K, 52Mn, 57Ni, and 208Tl. The identification of instrumental lines with specific isotopes is based on the line energies as well as on the variation of the event rate with time, cosmic-ray intensity, and deposited radiation dose during passages through the South-Atlantic Anomaly. The characteristic variation of the event rate due to a specific isotope depends on its life-time, orbital parameters such as the altitude of the satellite above Earth, and the solar cycle. A detailed understanding of the background contributions from instrumental lines is crucial at MeV energies for measuring the cosmic diffuse gamma-ray background and for observing gamma-ray line emission in the interstellar medium or from supernovae and their remnants. Procedures to determine the event rate from each background isotope are described, and their average activity in spacecraft materials over the first seven years of the mission is estimated.