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The first hyperpolarizability () of representative push-pull-conjugated compounds has been calculated at several levels of approximation to assess the effects of electron correlation. First, the 6-31G(d) basis set has been shown to give the best balance between accuracy and computational resources for a polyene linker whereas for polyyne linker, the 6-31G(d) basis set is already an optimal choice. As a result of cancellations between higher order contributions, the MP2 method turns out to be the method of choice to predict of push-pull-conjugated systems since it closely reproduces the values obtained with the reference CCSD(T) scheme. Moreover, the SDQ-MP4 and CCSD approaches provide rarely improved estimates over MP2 while the MP4 method does not represent an improvement over MP4-SDQ or the SCS-MP2 method, over MP2. Among density functional theory exchange-correlation functionals, LC-BLYP is reliable when characterizing the changes of first hyperpolarizability upon enlarging the-conjugated linker or upon changing the polyyne linker into a polyene segment. Nevertheless, its reliability is very similar to what can be achieved with the Hartree-Fock method and the MP2 scheme is by far more accurate. On the other hand, the BLYP, B3LYP, and BHandHLYP functionals perform quantitatively better in a number of cases but the trends are poorly described. This is also the case of the B2-PLYP and mPW2-PLYP functionals, which are often the most accurate, though they underestimate the increase of when going from polyyne to polyene linkers and overestimate the enhancement of with chain length.