The differential equations expressing the relations of velocity components and streamfunction for incompressible two-dimensional flow are typical one-degree-of-freedom Hamiltonian system. The streamfunction is expanded in Taylor series. The streamline patterns and their bifurcations are examined using methods from nonlinear system dynamics. Based on the small parameter canonical transformations in the physical flow plane, the normal form expressions of streamfunction and simplified differential equations are derived for the degenerate critical points. Some general characteristics of the simplified system are analyzed.