The intrinsic rheology of a fluid‐fluid interface has been found significant to multiphase flows for which surfactant material is present and the surface‐to‐volume ratio is large, such as in emulsification and demulsification, foam and emulsion stability, foam rheology, the dynamics of small bubbles or droplets, and interfacial mass transfer. An understanding of surface rheology therefore has practical relevance to engineering technologies wherein such phenomena occur: examples include the enhanced recovery of oil and the processing of food materials. Herein, a rheological theory is developed for a planar fluid surface which supercedes previous dynamic theories by explicitly acknowledging the nonlocal nature of the three‐dimensional interfacial transition zone. Beyond providing insight into the nature of the surface excess pressure tensor without the complicating features accompanying surface curvature, the treatment will provide a foundation for subsequent articles which will examine the rheology of curved surfaces possessing curvature as large as occurs in microemulsion systems. In the equilibrium state, the surface excess pressure tensor is shown to result from the highly inhomogeneous nature of the phase interface, whereas in the dynamic state a linear constitutive assumption results in the classical surface properties of surface viscosity and surface tension.