You should check the cluster/group in question that Mplus lists to see if there is a BETWEEN level variable whose values differ between individuals in that group. If that's the case, then it must be an error in the data as between level variables cannot have variation within groups/clusters. For example, company-level variables such as a company's size would take on the same value for all employees of a given company.

Dear Dr.Christian Geiser

Thanks for your tactful and complete response. I really appreciate your feedback.

Dear Christian Geiser I tried to run multilevel SEM using MPlus using large-scale assessment data. I have checked and there is not any between level variable whose values differ between individuals in that group. I am not sure why it still comes up "One or more between-level variables have variation within a cluster for the following clusters". You help is much appreciated! :)

Kason Ka Ching Cheung I would contact the Mplus support with your license number, data file, and Mplus input. I'm sure they can help you resolve this problem.