This paper focuses on 'mixed' delay-independent/delay-dependent asymptotic stability problems of a class of linear systems described by delay-differential equations involving several constant but unknown delays. We give some sufficient conditions for characterizing unbounded stability regions in the delays parameter space. The proposed approach makes use of some appropriate Liapunov-Krasovskii functionals, and the results obtained are expressed in terms of matrix inequalities. We also discuss several ways to construct such analytic functionals. These results allow us to recover (or to improve) as limit cases previous delay-independent or/and delay-independent conditions from the control literature.