The slow-scale stochastic simulation algorithm (ssSSA) proposed by Cao et al. [J. Chem. Phys. 122, 014116 (2005)] and the nested stochastic simulation algorithm (nSSA) proposed by E et al. [J. Chem. Phys. 123, 194107 (2005)] are closely related approximate simulation procedures aimed at speeding up the stochastic simulation of stiff chemical systems, i.e., systems that evolve through fast and slow dynamical modes with the fast mode being stable. This Comment aims to clarify some misconceptions that have arisen over the relationship between the ssSSA and the nSSA as regards both their theoretical foundations and their practical implementations. [ABSTRACT FROM AUTHOR]