In this paper, the μ-stability analysis issue of nonlinear differential systems along with two kinds of delay components, namely, leakage delay and transmission delay, is investigated. By constructing a suitable Lyapunov–Krasovskii's functional and utilizing Finsler's lemma, some novel μ-stability criteria for the concerned nonlinear system are obtained. These criteria are expressed in the framework of linear matrix inequalities (LMIs), which can be verified easily by means of standard software. Finally, two examples are presented to exhibit the advantage and effectiveness of the proposed theoretical results.