  For linear nonautonomous differential equations we introduce a new family of
spectrums defined with general nonuniform dichotomies: for a given growth rate
$\mu$ in a large family of growth rates, we consider a notion of spectrum,
named nonuniform $\mu$-dichotomy spectrum. This family of spectrums contain the
nonuniform dichotomy spectrum as the very particular case of exponential growth
rates. For each growth rate $\mu$, we describe all possible forms of the
nonuniform $\mu$-dichotomy spectrum, relate its connected components with
adapted notions of Lyapunov exponents, and use it to obtain a reducibility
result for nonautonomous linear differential equations. We also give an
illustrative examples where the spectrum is obtained, including a situation
where a normal form is obtained for polynomial behavior.
