Here, we take our first step to discover barriers to transport outside the idealized setting of temporally recurrent (steady, periodic or quasiperiodic) velocity fields. While we can no longer hope for even approximately recurring material surfaces in this general setting, we can certainly look for material surfaces that remain coherent. We perceive a material surface to be coherent if it preserves the spatial integrity without developing smaller scales. Those smaller scales would manifest themselves as protrusions from either side of the material surface without a break-up of that surface. In other words, using the terminology of the Introduction, we seek advective transport barriers in nonrecurrent flows as Lagrangian coherent structures (LCS). We will refer to this instantaneous limit of LCSs as objective Eulerian coherent structures (OECSs). These Eulerian structures act as LCSs over infinitesimally short time scales and hence their time-evolution is not material. Despite being nonmaterial, OECSs have advantages and important applications in unsteady flow analysis, as we will discuss separately.