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Delay-dependent/delay-independent uniform asymptotic stability and uniform stability criteria for linear systems with multiple timevarying delays are established respectively in this note. The results are derived based on a new-type stability theorem for retarded dynamical systems and a new analysis technique for estimating the derivative of a Lyapunov function along the solution of a system at certain specific instants. Four remarks together with an illustrative example are given to compare the obtained results with and to show their superiority to those in the literature. [ABSTRACT FROM AUTHOR]