  We study the maximum size of Sidon sets in unions of integers intervals. If
$A\subseteq\mathbb{N}$ is the union of two intervals and if $\left| A
\right|=n$ (where $\left| A \right|$ denotes the cardinality of $A$), we prove
that $A$ contains a Sidon set of size at least $0, 876\sqrt{n}$. On the other
hand, by using the small differences technique, we establish a bound of the
maximum size of Sidon sets in the union of $k$ intervals.
