# Article

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Keywords:
${\bold\Psi}$-boundedness; ${\bold\Psi}$-asymptotic equivalence
Summary:
In this paper new generalized notions are defined: ${\bold\Psi}$-boundedness and ${\bold\Psi}$-asymptotic equivalence, where ${\bold\Psi}$ is a complex continuous nonsingular $n\times n$ matrix. The ${\bold\Psi}$-asymptotic equivalence of linear differential systems $y'= A(t) y$ and $x'= A(t) x+ B(t) x$ is proved when the fundamental matrix of $y'= A(t) y$ is ${\bold\Psi}$-bounded.
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