The 1,3-dipolar cycloaddition reactions of diazomethane with ethylene and formaldehyde as well as the nitrogen elimination reactions from the cycloadducts have been studied using density functional and conventional ab initio methods. The exothermicity of the reactions is underestimated by DFT methods with respect to CCSD(T) due to an overestimation of the C-N dissociation energy of diazomethane. For the cycloaddition reactions all methods lead to similar transition state geometries, and the potential energy barriers computed using DFT methods are similar to the CCSD(T) ones. On the other hand, for the nitrogen elimination reactions transition state geometries and energy barriers are more dependent on the level of calculation. The results obtained show that for the reaction between diazomethane and ethylene the pyrazoline intermediate is more stable than the reactants and that the Gibbs energy barrier for nitrogen elimination is larger than the barrier corresponding to its formation. On the contrary, for formaldehyde the kinetically most favorable cycloadduct, 1,2,3-oxadiazoline, is less stable than the reactants and has a lower barrier for nitrogen elimination.