  Following earlier results of Sondow, we propose another criterion of
irrationality for Euler's constant $\gamma$. It involves similar linear
combinations of logarithm numbers $L\_{n,m}$. To prove that $\gamma$ is
irrational, it suffices to prove that, for some fixed $m$, the distance of
$d\_n L\_{n,m}$ ($d\_n$ is the least common multiple of the $n$ first integers)
to the set of integers $\mathbf{Z}$ does not converge to 0. A similar result is
obtained by replacing logarithms numbers by rational numbers: it gives a
sufficient condition involving only rational numbers. Unfortunately, the
chaotic behavior of $d\_n$ is an obstacle to verify this sufficient condition.
All the proofs use in a large manner the theory of Pad\'e approximation.
