In this paper, we study the powers of two important classes of graphs — strongly chordal graphs and circular arc graphs. We show that for any positive integer \(k \geq 2\), \(G^{k-1}\) is a strongly chordal graph implies \(G^k\) is a strongly chordal graph. In case of circular arc graphs, we show that every integral power of a circular arc graph is a circular arc graph.