3C 66A is an intermediate-frequency-peaked BL Lac object detected by the Large Area Telescope onboard the Fermi Gamma-ray Space Telescope. We present a study of the long-term variations of this blazar seen over 2 years at GeV energies with Fermi and in the optical (flux and polarization) and near infrared with the Kanata telescope. In 2008, the first year of the study, we find a correlation between the gamma-ray flux and the measurements taken with the Kanata telescope. This is in contrast to the later measurements performed during 2009--2010 which show only a weak correlation along with a gradual increase of the optical flux. We calculate an external seed photon energy density assuming that the gamma-ray emission is due to external Compton scattering. The energy density of the external photons is found to be higher by a factor of two in 2008 compared to 2009--2010. We conclude that the different behaviors observed between the first year and the later years might be explained by postulating two different emission components. ; Comment: 9 pages, 10 figures