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The stability and asymptotic properties of a real 2n-dimensional system x' = A(t)x + h(t, x) are studied. Here A(t) is a square block-diagonal matrix with blocks of order two and h(t,x) is a vector function. The method is based on the combination of the technique of complexification and that of vector Lyapunov functions. Stability and asymptotic properties 699 Hence Zj = (a 2 j-l,2j-lX2j-l + 0-2j-l,2j x 2j + h 2 j-l)+ + »( a 2j,2j-l®2i-l + + h2j) = = (o2i-i,2j-i + ia 2 j,2j-i)x2j-i + (a 2doi:10.1515/dema-1997-0401 fatcat:7mw757ca3fg6jgynvuhv7yl4ny