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The problem of posing and solving ordinary differential equations on supermanifolds is addressed from the point of view of Lie’s theory. It is shown that no nonsingular, nondegenerate, odd supervector field can have a Lie supergroup action of      R 1 | 1 {{\mathbf {R}}^{1|1}}       as its flow. It is also shown that the class of integrable supervector fields goes far beyond homogeneity and rectifiability. The obstructions for the integral flow to be an      R 1 | 1 {{\mathbf {R}}^{1|1}}      -action are given by the Lie superbracket of the field with itself and the Lie bracket of its homogeneous components.

𝑅^{1|1}-supergroup actions and superdifferential equations