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The linear and nonlinear optical (NLO) properties of a series of Λ -shaped derivatives containing a 4,5-dicyanopyrazine acceptor unit, N,N -dimethylamino donor groups and systematically enlarged π-conjugated linkers are investigated by means of UV/Visible and Hyper-Rayleigh scattering spectroscopies. Density functional theory calculations are also carried out to rationalize the magnitude and symmetry of the NLO responses. The results demonstrate that these compounds possess two low-lying excited electronic states close to each other in energy, which are accessible through one-photon optical transitions respectively polarized perpendicular and parallel to the two-fold molecular axis. These two states contribute additively to the first hyperpolarizability, which exhibits a dominant dipolar character. We also show that the NLO responses significantly deviate from Kleinman's index permutation symmetry. • Λ -shaped pyrazine derivatives deliver strong second-order NLO responses. • They result from the contribution of low-lying perpendicular electronic transitions. • The first hyperpolarizabilities are not Kleinman-symmetric. • These second-order NLO responses have a dominant dipolar character. • Their amplitudes depend on the nature of the π-conjugated linkers. [ABSTRACT FROM AUTHOR]