Let G be the circulant graph Cn.S/ with S ⊂ f1; 2; : : : ; b n 2 cg, and let I .G/ denote the edge ideal in the polynomial ring R D KTx0; x1; : : : ; xn-1U over a field K. In this paper we compute the N- graded Betti numbers of the edge ideals of three families of circulant graphs Cn.1; 2; : : : ;bj ; : : : ; b n 2 c/, Clm.1; 2; : : : ; b2l; : : : ; b3l; : : : ; blm 2 c/ and Clm.1; 2; : : : ;bl ; : : : ; b2l; : : : ; b3l; : : : ; blm 2 c/. Other algebraic and combinatorial properties like regularity, projective dimension, induced matching number and when such graphs are well-covered, Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum and S2 are also discussed.