Summary: We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities
\[ (\partial^2_t-\partial^2_x+m^2_j)u_j={\mathcal N}_j(\partial u), \]
\(j = 1,\dots,l\). We show the existence of solutions in an analytic function space. When the nonlinearity satisfies a strong null condition introduced by Georgiev we prove the global existence and obtain the large time asymptotic behavior of small solutions.