Simulation results are often limited to mean values, even though this provides very limited information about the analyzed systems' performance. Quantile analysis provides much deeper insights into the performance of simulation system of interest. A set of quantiles can be used to approximate a cumulative distribution function, providing full information about a given performance characteristic of the simulated system. In this paper, we will present two methods for parallel sequential estimation of steady state quantiles. The quantiles are estimated using simulation output data from concurrently executed independent replications. They are calculated sequentially and on-line, i.e. during simulation, to ensure that the results are produced to a specified accuracy. The set of quantiles to be estimated can be automatically determined using efficient estimation as a criterion.