The evolution of the velocity and magnetic fields associated with supergranulation has been investigated using the Sacramento Peak Observatory Diode Array Magnetograph. The observations consist of time sequences of simultaneous velocity, magnetic field, and chromospheric network measurements. From these data it appears that the supergranular velocity cells have lifetimes in excess of 30 h. Magnetic field motions associated with supergranulation were infrequent and seem to be accompanied by changes in the velocity field. More prevalent was the slow dissipation and diffusion of stationary flux points. These observations suggest that surface motions do not exhibit the detailed flux redistribution expected in the random-walk diffusion of magnetic fields. It is suggested that the surface motions are only the reflection of magnetic field-convective motion interactions which occur deeper in the convection zone.