  We present a first study of gluonic twist-four corrections to the deep
inelastic structure function F_2 at small x and small Q^2. The calculations are
based upon the double logarithmic approximation of the coupled twist-four
evolution equations of the gluonic twist-four operators that are expected to be
dominant at small x. We first review the analytical results which are presently
available and define the framework of our calculation. In the second part we
discuss the connection with DIS diffractive dissociation which can be used to
estimate the size of some of the twist-four corrections. In the final part we
show, for three different choices of the input distributions, the relative
magnitude of the leading-twist and the twist-four contributions.
