In this paper, we consider the problem of tracking multiple quantiles of dynamically varying data stream distributions. The method is based on making incremental updates of the quantile estimates every time a new sample is received. The method is memory and computationally efficient since it only stores one value for each quantile estimate and only performs one operation per quantile estimate when a new sample is received from the data stream. The estimates are realistic in the sense that the monotone property of quantiles is satisfied in every iteration. Experiments show that the method efficiently tracks multiple quantiles and outperforms state-of-the-art methods.