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In this paper we present a classification, up to equivariant isomorphism, of 
${{C}^{*}}$-dynamical systems 
$(A,\,\mathbb{R},\,\alpha )$ arising as inductive limits of directed systems 
$\{({{A}_{n}},\,\mathbb{R},\,{{\alpha }_{n}}),\,{{\varphi }_{nm}}\}$, where each 
${{A}_{n}}$ is a finite direct sum of matrix algebras over the continuous functions on the unit circle, and the 
${{\alpha }_{n}}\text{s}$ are outer actions generated by rotation of the spectrum.
