  We obtain a necessary and sufficient condition for the linear independence of
solutions of differential equations for hyperlogarithms. The key fact is that
the multiplier (i.e. the factor $M$ in the differential equation $dS=MS$) has
only singularities of first order (Fuchsian-type equations) and this implies
that they freely span a space which contains no primitive. We give direct
applications where we extend the property of linear independence to the largest
known ring of coefficients.
