Seven-month records of current and temperature measurements from a moored array centered at 53¿E on the equator in the Indian Ocean are consistent with a continuous spectrum of equatorially trapped internal inertial-gravity, mixed Rossby-gravity, and Kelvin waves. A model spectrum of free linear waves analogous to those for mid-latitude internal gravity waves is used to compute spectra of observed quantities at depths greater than about 2000 m. Model parameters are adjusted to fit general patterns in the observed spectra over periods from roughly 2 days to 1 month. Measurements at shallower depths presumably include forced motions which we have not attempted to model. This 'straw-person' spectrum is consistent with the limited data available. The model spectrum ?(n,m,ω)=K⋅B(m)⋅C(n,ω), where ? is an average local energy density in the equatorial wave guide which has amplitude K, wave number shape B(m)∝(1+m/m*)-3, where m is vertical mode number and the bandwidth parameter m* is between 4 and 8, and frequency shape C(n,ω)∝<(2n+1+s2)1/2⋅&sgr;3>-1 where n is meridional mode number, and s and &sgr; are dimensionless zonal wave number and frequency related by the usual dispersion relation. The scales are (β/cm)1/2 and (β⋅cm1/2 for horizontal wave number and frequency, where cm is the Kelvin wave speed of the vertical mode m. At each frequency and vertical wave number, energy is partitioned equally among the available inertial gravity modes so that the field tends toward horizontal isotropy at high frequency. The transition between Kelvin and mixed Rossby-gravity motion at low frequency and inertial-gravity motion at high frequency occurs at a period of roughly 1 week. At periods in the range 1--3 weeks, the model spectrum which fits the observations suggests that mixed Rossby-gravity motion dominates; at shorter periods gravity motion dominates. The model results are consistent with the low vertical coherence lengths observed (roughly 80 m). Horizontal coherence over 2 km is consistent with isotropic energy flux. Evidence for net zontal energy flux is not found in this data, and the presence of a red wave number shape suggests that net flux will be difficult to observe from modest moored arrays. The equatorial wave spectrum does not match across the diurnal and semidiurnal tides to the high-frequency internal wave spectrum (the latter is roughly 1 decade higher).