In this paper, the theory of Oᵣ-convergence and weak Oᵣ-convergence of nets is introduced in L-topological spaces by means of neighborhoods and strong neighborhoods of fuzzy points based on Shi’s O-convergence.It can be used to characterize preclosed sets, preopen sets, δ-closed sets, δ-open sets, near compactness and near S∗-compactness.