  A representation in the form of spectral parameter power series (SPPS) is
given for a general solution of a one dimension Dirac system containing
arbitrary matrix coefficient at the spectral parameter, \[ B \frac{dY}{dx} +
P(x)Y = \lambda R(x)Y,\] where $Y=(y_1,y_2)^T$ is the unknown vector-function,
$\lambda$ is the spectral parameter, $B = \begin{pmatrix}0 & 1 \\ -1 &
0\end{pmatrix}$, and $P$ is a symmetric $2\times 2$ matrix, $R$ is an arbitrary
$2\times 2$ matrix whose entries are integrable complex-valued functions. The
coefficient functions in these series are obtained by recursively iterating a
simple integration process, beginning with a non-vanishing solution for one
particular $\lambda = \lambda_0$. The existence of such solution is shown.
  For a general linear system of two first order differential equations \[
  P(x)\frac{dY}{dx}+Q(x)Y = \lambda R(x)Y,\ x\in [a,b], \] where $P$, $Q$, $R$
are $2\times 2$ matrices whose entries are integrable complex-valued functions,
$P$ being invertible for every $x$, a transformation reducing it to a type
considered above is shown.
  The general scheme of application of the SPPS representation to the solution
of initial value and spectral problems as well as numerical illustrations are
provided.
