The present invention relates to a composition comprising an oil phase and a fibrous preparation of delaminated cell wall material dispersed in said oil phase, wherein the cell wall material is sourced from plant tissue, and wherein said fibrous preparation has a specific surface area corresponding to an SBET of at least 5 m2/g. The invention also relates to a method to prepare such compositions and the use of said cell wall material to structure the oil phase of a composition comprising an oil phase.