2-Methyl-4H-pyrido[2,3-d][1,3]oxazin-4-one (III) was reacted with amines IVa-j to give corresponding 2-methyl-3H-pyrido[2,3-d]pyrimidin-4-ones (Va-j) substituted at position 3. These reactions afforded non-cyclic by-products VIa', VIg', and VIh' which were converted into compounds Va, Vg and Vh by the action of POCl3. Structures of the newly obtained compounds have been confirmed by elemental analysis for C, H and N, and by IR and 1H NMR spectra.