  Embeddings of pairs of disjoint nonparallel primitive simple closed curves in
the boundary of a genus two handlebody are classified. Briefly, two disjoint
primitives either lie on opposite ends of a product $F \boldsymbol{\times} I$,
or they lie on opposite ends of a kind of "twisted" product $F
\widetilde{\boldsymbol{\times}} I$, where $F$ is a once-punctured torus. If one
of the curves is a proper power of a primitive, the situation is simpler.
Either the curves lie on opposite sides of a separating disk in the handlebody,
or they bound a nonseparating essential annulus in the handlebody.
