Magnetic reconnection due to electron inertia is responsible for fast and violent phenomena in magnetized plasmas in which magnetic energy is converted into electron kinetic energy on very short timescales. To study the nonlinear evolution of a reconnecting mode, the collisionless two-fluid drift-Alfvén equations are applied to an equilibrium that consists of a z-independent, cylindrically symmetric current region, with jumps in the radial direction. The Lagrangian advective formulation of the two-fluid equations makes it possible to use the powerful contour dynamics (CD) method to study linear stability and calculate numerically the nonlinear evolution of a tearing unstable equilibrium using a two-fluid model. The analytical expressions obtained for the linear dispersion relation are in good agreement with the CD simulations.