  The Atacama Cosmology Telescope has measured the angular power spectra of
microwave fluctuations to arcminute scales at frequencies of 148 and 218 GHz,
from three seasons of data. At small scales the fluctuations in the primordial
Cosmic Microwave Background (CMB) become increasingly obscured by extragalactic
foregounds and secondary CMB signals. We present results from a nine-parameter
model describing these secondary effects, including the thermal and kinematic
Sunyaev-Zel'dovich (tSZ and kSZ) power; the clustered and Poisson-like power
from Cosmic Infrared Background (CIB) sources, and their frequency scaling; the
tSZ-CIB correlation coefficient; the extragalactic radio source power; and
thermal dust emission from Galactic cirrus in two different regions of the sky.
In order to extract cosmological parameters, we describe a likelihood function
for the ACT data, fitting this model to the multi-frequency spectra in the
multipole range 500<ell<10000. We extend the likelihood to include spectra from
the South Pole Telescope at frequencies of 95, 150, and 220 GHz. Accounting for
different radio source levels and Galactic cirrus emission, the same model
provides an excellent fit to both datasets simultaneously, with chi2/dof=
675/697 for ACT, and 96/107 for SPT. We then use the multi-frequency likelihood
to estimate the CMB power spectrum from ACT in bandpowers, marginalizing over
the secondary parameters. This provides a simplified `CMB-only' likelihood in
the range 500<ell<3500 for use in cosmological parameter estimation.
