Some aspects of plasma dynamics with electron-inertia effects are considered. The behaviour of (i) one-dimensional steady current sheets, (ii) two-dimensional steady reconnection models, (iii) one-dimensional current-sheet evolution, (iv) linear tearing-mode evolution and (v) nonlinear magnetic-island evolution in this regime is investigated. Stability of the two-dimensional plasma in this regime is then discussed, and necessary conditions for linear stability in the Liapunov sense for steady states are then given.