  We study general (not necessarily Hamiltonian) first-order symmetric systems
$J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b\rangle $ with the regular
endpoint $a$. It is assumed that the deficiency indices $n_\pm(\Tmi)$ of the
minimal relation $\Tmi$ satisfy $n_+(\Tmi)< n_-(\Tmi)$. We define
  $\l$-depending boundary conditions which are analogs of separated
self-adjoint boundary conditions for Hamiltonian systems. With a boundary value
problem involving such conditions we associate an exit space self-adjoint
extension $\wt T$ of $\Tmi$ and the $m$-function $m(\cd)$, which is an analog
of the Titchmarsh-Weyl coefficient for the Hamiltonian system. By using
$m$-function we obtain the eigenfunction expansion with the spectral function
$\Si(\cd)$ of the minimally possible dimension and characterize the case when
spectrum of $\wt T$ is defined by $\Si(\cd)$. Moreover, we parametrize all
spectral functions in terms of a Nevanlinna type boundary parameter.
Application of these results to ordinary differential operators of an odd order
enables us to complete the results by Everitt and Krishna Kumar on the
Titchmarsh-Weyl theory of such operators.
