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The Eulerian and Lagrangian second-order perturbation theories are solvedexplicitly in closed forms in $\Omega \neq 1$ and $\Lambda \neq 0${}Friedmann-Lema\^{\i}tre models. I explicitly write the second-order theoriesin terms of closed one-dimensional integrals. In cosmologically interestedcases ($\Lambda = 0$ or $\Omega + \lambda = 1$), they reduce to elementaryfunctions or hypergeometric functions. For arbitrary $\Omega$ and $\Lambda$, Ipresent accurate fitting formula which are sufficient in practice for theobservational cosmology. It is reconfirmed for generic $\Omega$ and $\Lambda$of interest that second-order effect only weakly depends on these parameters.Comment: 9 pages, LaTeX, to appear in Progress of Theoretical Physics  (Letters

On Second-Order Perturbation Theories of Gravitational Instability in Friedmann-Lemaitre Models