  We study general (not necessarily Hamiltonian) first-order symmetric system
$J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b) $ with the regular endpoint
$a$ and singular endpoint $b$. It is assumed that the deficiency indices
$n_\pm(\Tmi)$ of the corresponding minimal relation $\Tmi$ in $\LI$ satisfy
$n_-(\Tmi)\leq n_+(\Tmi)$. We describe all generalized resolvents $y=R(\l)f, \;
f\in\LI,$ of $\Tmi$ in terms of boundary problems with $\l$-depending boundary
conditions imposed on regular and singular boundary values of a function $y$ at
the endpoints $a$ and $b$ respectively. We also parametrize all characteristic
matrices $\Om(\l)$ of the system immediately in terms of boundary conditions.
Such a parametrization is given both by the block representation of $\Om(\l)$
and by the formula similar to the well-known Krein formula for resolvents.
These results develop the \u{S}traus' results on generalized resolvents and
characteristic matrices of differential operators.
