  In this paper we obtain the explicit expression of the Green's function
related to a general $n$ order differential equation coupled to non-local
linear boundary conditions. In such boundary conditions, a $n$ dimensional
parameter dependence is also assumed. Moreover, some comparison principles are
obtained.
  The explicit expression depends on the value of the Green's function related
to the two-point homogeneous problem, that is, we are assuming that when all
the parameters involved on the boundary conditions take the value zero then the
problem has a unique solution which is characterized by the corresponding
Green's function $g$. The expression of the Green's function $G$ of the general
problem is given as a function of $g$ and the real parameters considered at the
boundary conditions.
  It is important to show that, in order to ensure the uniqueness of solutions
of the linear considered problem, we must assume a non resonant additional
condition on the considered problem, which depends on the non local conditions
and the corresponding parameters.
  We point out that the assumption of the uniqueness of solutions of the
two-point homogeneous problem is not a necessary condition to ensure the
solution of the general case. Of course, in this situation the expression we
are looking for must be obtained in a different manner.
  To show the applicability of the obtained results, a particular example is
given.
