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The integrability of a system of two symmetrically coupled higher-ordernonlinear Schr\"{o}dinger equations with parameter coefficients is tested bymeans of the singularity analysis. It is proven that the system passes thePainlev\'{e} test for integrability only in ten distinct cases, of which twoare new. For one of the new cases, a Lax pair and a multi-field generalizationare obtained; for the other one, the equations of the system are uncoupled by anonlinear transformation.Comment: 12 pages, LaTeX2e, IOP style, final version, to appear in  J.Phys.A:Math.Ge

Symmetrically coupled higher-order nonlinear Schrödinger equations: singularity analysis and integrability