Compared　to　general　multi-objective　optimization　problems,　multimodal　multi-objective　optimization　problems　(MMOPs)　with　local　Pareto　sets　(PSs)　must　determine　multiple　global　and　local　PSs　simultaneously.　Therefore,　MMOPs　with　local　PSs　are　challenging.　To　resolve　this　issue,　this　study　proposes　a　multimodal　multi-objective　optimization　evolutionary　algorithm　based　on　two-stage　species　conservation　(MMOEA/TSC).　MMOEA/TSC　divides　the　evolutionary　process　into　two　stages:　diversity-oriented　species　conservation　and　convergence-oriented　species　conservation.　The　former　is　aimed　at　locating　promising　regions　in　which　global　and　local　PSs　may　exist.　To　balance　the　distribution　of　solutions,　a　Gaussian　variation　strategy　is　used　to　iteratively　generate　diverse　offspring　in　regions　that　contain　the　smallest　number　of　solutions.　The　latter　mainly　focused　on　obtaining　one　PS　with　good　convergence　in　each　promising　region.　To　help　the　solutions　converge　to　the　global　and　local　PSs　uniformly,　a　species　stratification　strategy　was　adopted　according　to　the　Pareto　level　of　the　well-converged　solution　for　each　species.　The　proposed　algorithm　was　compared　with　seven　state-of-the-art　algorithms.　For　the　CEC　2020　MMOP　test　problem　set,　the　experimental　results　show　that　MMOEA/TSC　has　the　capacity　to　find　global　and　local　PSs.　©　2023　Elsevier　Inc.