We present a relation between mu -dichotomy spectrum and Sacker-Sell spectrum. From this relation, we show that, under some suitable conditions, if the system x' = A(t)x admits a mu dichotomy, then it admits an exponential dichotomy. Utilizing this result, we present a linearization theorem. Furthermore, we prove that the mu -dichotomy spectrum of the system x' = diag(A1(t), A2(t))x is the union of mu -dichotomy spectra of the subsystems x'1 = A1(t)x1 and x'2 = A2(t)x2, while this result is wrong if we replace mu -dichotomy spectrum with nonuniform exponential dichotomy spectrum. We also provide a new method to prove the mu -dichotomy spectral theorem. (c) 2024 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.