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We solve the complex Einstein equations for Bianchi I and II modelsformulated in the Ashtekar variables. We then solve the reality conditions toobtain a parametrization of the space of Lorentzian solutions in terms of realcanonically conjugate variables. In the Ashtekar variables, the dynamics of theuniverse point particle is governed by only a curved supermetric -- there is nopotential term. In the usual metric formulation the particle bounces off apotential wall in flat superspace. We consider possible characterizations ofthis ``bounce'' in the potential-free Ashtekar variables.Comment: Latex, uses revtex, 13 pages in 10p

Classical analysis of Bianchi types I and II in Ashtekar variables