  Einstein's field equations for stationary Bianchi type II models with a
perfect fluid source are investigated. The field equations are rewritten as a
system of autonomous first order differential equations. Dimensionless
variables are subsequently introduced for which the reduced phase space is
compact. The system is then studied qualitatively using the theory of dynamical
systems. It is shown that the locally rotationally symmetric models are not
asymptotically self-similar for small values of the independent , tovariable. A
new exact solution is also given.
