  We investigate the \textit{irregularity strength} ($s(G)$) and \textit{total
vertex irregularity strength} ($tvs(G)$) of circulant graphs $Ci_n(1,2,...,k)$
and prove that $tvs(Ci_n(1,2,...,k))=\lceil\frac{n+2k}{2k+1}\rceil$, while
$s(Ci_n(1,2,...,k))=\lceil\frac{n+2k-1}{2k}\rceil$ except the case when $(n
\bmod 4k = 2k+1 \wedge k\bmod 2=1) \vee n=2k+1$ and
$s(Ci_n(1,2,...,k))=\lceil\frac{n+2k-1}{2k}\rceil+1$.

Combinatorics