A spherical harmonic model of the planetary magnetic field of Neptune is obtained from the Voyager 2 encounter observations. The model is obtained by partial solution to the underdetermined inverse problem (eighth-order and degree spherical harmonic model) using generalized inverse techniques. Dipole and quadrupole Schmidt-normalized spherical harmonic coefficients are determined, or resolved, independently of higher-order terms. Much additional information is also obtained regarding octupole and higher-order components of the field. Model parameter resolution and uniqueness are addressed using new visual representations of the ''resolution matrix.'' The model yields a dipole of magnitude 0.14 G R3N, tilted by 47¿ toward 72¿ west longitude. Nepture's quadrupole is relatively large, equal to or exceeding in magnitude the (surface) dipole field. The octupole is likewise very large but less well constrained. The magnetic fields of Neptune and Uranus are very much alike and equally unlike those of the other known magnetized planets. Characteristics of this complex magnetic field are illustrated, using contour maps of the field on the planet's surface, and discussed in the context of dynamo generation in the relatively poorly conducting ''ice mantle.'' ¿ American Geophysical Union 1991