This paper studies -efficiency in multiobjective optimization by using the so-called coradiant sets. Motivated by the nonlinear separation property for cones, a similar separation property for coradiant sets is investigated. A new notion, called Bishop-Phelps coradiant set is introduced and some appropriate properties of this set are studied. This paper also introduces the notions of -dual and augmented -dual for Bishop and Phelps coradiant sets. Using these notions, some scalarization and characterization properties for -efficient and proper -efficient points are proposed.