Electronic Journal of Differential Equations, Vol. 2009(2009), No. 35, pp. 1-16. Title: Stability for a family of systems of differential equations with sectionally continuous right-hand sides Authors: Acacio da Conceicao de Jesus Domingos (Univ. Agostinho Neto, Angola) Gilner de la Hera Martinez (Univ. de Las Tunas, Cuba) Efren Vazquez Silva (Univ. of Informatics Sciences, Havana, Cuba) Abstract: In this work, we obtain necessary and sufficient conditions to guarantee the asymptotic stability of the trivial solution for a family of interconnected 2X2 systems of differential equations Submitted May 2, 2008. Published February 25, 2009. Math Subject Classifications: 34K20, 34K25. Key Words: Interconnecting systems; stability.