The objective of this paper is to construct some unbiased estimators of the current population mean in two-occasion successive sampling. Utilizing the readily available information on an auxiliary variable on both occasions, almost unbiased ratio and regression cum exponential type estimators of current population mean have been proposed. Theoretical properties of the proposed estimation procedures have been examined and their respective optimum replacement strategies are formulated. Performances of the proposed estimators are empirically compared with (i) the sample mean estimator, when no sample units were matched from the previous occasion and (ii) natural successive sampling estimator when no auxiliary information was used on any occasion. Empirical results are critically interpreted and suitable recommendations are made to the survey practitioners for their practical applications.