Algorithm 1007: QNSTOP Quasi-Newton Algorithm for Stochastic Optimization. QNSTOP consists of serial and parallel (OpenMP) Fortran 2003 codes for the quasi-Newton stochastic optimization method of Castle and Trosset. For stochastic problems, convergence theory exists for the particular algorithmic choices and parameter values used in QNSTOP. Both the parallel driver subroutine, which offers several parallel decomposition strategies, and the serial driver subroutine can be used for stochastic optimization or deterministic global optimization, based on an input switch. QNSTOP is particularly effective for “noisy” deterministic problems, using only objective function values. Some performance data for computational systems biology problems is given.