The group of extensions Ext(A, Ga
) and Ext(A, Gm
) of an abelian variety A by the additive or multiplicative group Ga, Gm
have been investigated in detail (, , [GACC]). On the other hand, F. Oort  and M. Miyanishi  recently studied the groups Ext(Ga, A) and Ext(Gm, A). The purpose of the present paper is to clarify the relationship between these groups. Our results show that the latter groups can be derived from the former.