This paper deals with systems of ordinary differential equations \[ y^{(n)}+P(t)y=0,\tag{1} \] where \(P(t)\) is a continuous \(n\times n\)-matrix, \(t\in j=[a,\omega)\), \(\omega\leq\infty\). The main result is the following: Let \( P(t) \) be a continuous and selfadjoint matrix; \(\lambda_{i}(t),i=1,\ldots,n\), be eigenvalues of matrix \(P(t)\). Then system (1) is a nonoscillating system on the interval \(j\) if and only if the scalar equations \(v^{(n)}+\lambda_i(t)v=0,i=1,\ldots,n\), are nonoscillating equations on this interval.