  We develop a Hamilton-Jacobi-like formulation of Nambu mechanics. The Nambu
mechanics, originally proposed by Nambu more than four decades ago, provides a
remarkable extension of the standard Hamilton equations of motion in even
dimensional phase space with a single Hamiltonian to a phase space of three
(and more generally, arbitrary) dimensions with two Hamiltonians (n
Hamiltonians in the case of (n+1)-dimensional phase space) from the viewpoint
of the Liouville theorem. However, it has not been formulated seriously in the
spirit of Hamilton-Jacobi theory. The present study is motivated to suggest a
possible direction towards quantization from a new perspective.
