  Stability of the zero solution plays an important role in the investigation
of positive systems. In this note, we revisit the $\mu$-stability of positive
nonlinear systems with unbounded time-varying delays. The system is modelled by
continuous-time differential equations. Under some assumptions on the nonlinear
functions like homogeneous, cooperative, nondecreasing, we propose a novel
transform, by which the nonlinear system reduces to a new system. Thus, we
analyze its dynamics, which can simplify the nonlinear homogenous functions
with respect to (w.r.t.) arbitrary dilation map to those w.r.t. the standard
dilation map. We finally get some criteria for the global $\mu$-stability. A
numerical example is given to demonstrate the validity of obtained results.
