Let p, q and s be three different prime integers. Let \(\ell \ge 1\) be a positive odd square-free integer relatively prime to p, q and s. The purpose of this paper is to show how one can proceed to perform the calculation of unit group of the fields of the form \(\mathbb {L}^+=\mathbb {Q}(\sqrt{2}, \sqrt{pq}, \sqrt{ps})\) and \(\mathbb {L}=\mathbb {Q}(\sqrt{2}, \sqrt{pq}, \sqrt{ps}, \sqrt{-\ell })\) . More precisely, we compute the unit group and the 2-class number of these fields whenever \(p\equiv -q\equiv -s\equiv 5\pmod 8\) and \(\left( \frac{ p}{ q}\right) =\left( \frac{ p}{ s}\right) ,\) or \(p\equiv q\equiv s\equiv 3\pmod 8\) .
