We discuss self-phase modulations and related transverse effects accompanying interaction of a light beam with a second harmonic radiation generated by it. Some experimental observations are explained by a simple perturbative approach. Numerical simulations provide a further insight into the nature of transverse self-effects in quadratically nonlinear media. An effective x (3)-like behaviour of dispersive quadratically nonlinear media is discussed. Such feature may lead to important consequences for measurements of the x (3) tensor in complex nonlinear media.