An important result obtained from solar observations made in coronal e
mission lines has been to establish the existence of periodic oscillat
ions or waves in the corona. These are detected, although not always s
imultaneously, in line intensity, line-width or Doppler velocity with
oscillation periods of several minutes. For this reason, we have studi
ed the magnetohydrodynamic modes of oscillation of a coronal potential
arcade under different boundary conditions, solving the wave equation
s for different density profiles. Our results show that only the Alfve
n and the fast mode exist in such a structure and that the slow mode i
s absent, because of the assumed low-beta limit. The Alfven mode produ
ces a continuous spectrum of frequencies with periods which can vary f
rom zero to infinity, depending on the assumed density profile. Due to
the polarization direction of the plasma motions, these waves could i
n principle be detected in front-view observations of coronal arcades
at the limb. Concerning the fast mode, we have obtained several diagno
stic diagrams using different density profiles and boundary conditions
. These diagrams would be useful for comparing the predicted and obser
ved periods. However, the observational identification of fast modes c
ould be harder since we would need lateral observations of the coronal
arcades.