An analysis shows that hydrodynamic instabilities of two-phase flow are classified into at least eight types. Three of them are roughly classified into the static or the Ledinegg instability, and other five of them into the dynamic or the density wave instability. Two typical types of instabilities are observed in our experiment, in each type different pressure drop term: gravitational or frictional pressure drop of two-phase flow is found to be the governing term. Classification method of instabilities and its applications are presented.