A two-dimensional dynamical system is proposed that is described by a pair of nonlinear ordinary differential equations(ODEs) with a complex parameter. It reduces to Abel’s nonlinear ODE of the first kind by an appropriate transformation. Using this fact the properties of solutions are investigated in detail with the aid of numerical computations. It is found that various types of bifurcation phenomena occur depending on the values of the parameter. In particular, the solution is shown to blow up in finite time under certain conditions. In order to visualize the behaviors of dynamical motions the trajectories of solutions are depicted in the plane. Finally, a discussion is made on some generalizations of the proposed system.