This paper aims at identifying profiles of students that are homogenous with regard to their ability to solve Complex Problem Solving (CPS) tasks, as assessed by the MicroDYN approach, a computer test made of 9 independent tasks, and administered to a sample of 6th and 9th grade Finnish students. For this aim, we estimate a discrete two-tier Item Response Theory (IRT) model. Results indicate that: (1) the conceptualisation of CPS as a three-dimensional variable is reasonable and (2) there are seven latent classes of students characterised by a specific profile with regard to the adopted CPS strategies, with students clustered in the higher la- tent classes having generally a higher CPS ability than the others, across the three CPS dimensions.