  The collective charge-excitation spectrum of a double quantum well system in
a strong magnetic field is obtained within the random phase approximation.
Correction to the spectrum coming from the finiteness of the magnetic field is
calculated up to the first order in inverse of the magnetic field. Dependencies
on the magnetic field of (i) the velocity of long wave length excitation and
(ii) the phase boundary of the quantum Hall state signaled by the softening of
the roton minimum of the spectrum are discussed. Keywords: quantum Hall effect,
two dimensional electrons, strong magnetic field, double quantum well,
excitonic state
