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A representation in the form of spectral parameter power series (SPPS) isgiven for a general solution of a one dimension Dirac system containingarbitrary 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. Thecoefficient functions in these series are obtained by recursively iterating asimple integration process, beginning with a non-vanishing solution for oneparticular $\lambda = \lambda_0$. 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 typeconsidered above is shown.  The general scheme of application of the SPPS representation to the solutionof initial value and spectral problems as well as numerical illustrations areprovided.

Spectral parameter power series representation for solutions of linear system of two first order differential equations