This chapter gives an overview of non-Gaussian random-effects modeling in the context of finite-mixture growth modeling developed in Muthe´n and Shedden (1999), Muthe´n (2001a, 2001b, 2004), and Muthe´n et al. (2002), and extended to cluster samples and clusterlevel mixtures in Asparouhov and Muthe´n (2008). Growth mixture modeling represents

unobserved heterogeneity between the subjects in their development using both random effects (e.g., Laird and Ware, 1982) and finite mixtures (e.g., McLachlan and Peel, 2000). This allows different sets of parameter values for mixture components corresponding to different unobserved subgroups of individuals, capturing latent trajectory classes with different growth curve shapes. This chapter discusses examples motivating modeling with such trajectory classes. A general latent-variable modeling framework is presented together with its maximum likelihood estimation. Examples from criminology, mental health, and education are analyzed. The choice of a normal or a non-parametric distribution for the random effects is discussed and investigated using a simulation study. The discussion will refer to growth mixture modeling techniques as implemented in the Mplus program (Muthe´n and Muthe´n, 1998-2007) and input scripts for the analyses are available at https://www.statmodel.com.