In　this　paper,　we　consider　a　system　of　nonlinear　differential　equations　in　a　Banach　space　with　boundary　conditions　on　an　infinite　interval　and　provide　sufficient　conditions　for　the　existence　of　solutions　of　the　system.　Our　method　relies　upon　the　properties　of　the　Kuratowski　noncompactness　measure　and　the　Sadovskii　fixed　point　theorem.　An　example　is　given　to　illustrate　the　main　results.