UNLABELLED: Harmonizing the scores obtained by different instruments that measure the same construct enable researchers to combine them in one analysis. An important step in harmonization is checking whether there is measurement invariance across populations. This study aimed to examine whether the harmonized scores for anxiety/depression and ADHD obtained by two different instruments (the Child Behaviour Check List (CBCL) and the Strength and Difficulties Questionnaire (SDQ)) are measurement invariant across other countries, languages, and age groups. We used cohorts from Australia (1330 children aged 10-11.5 years), the Netherlands (943 children aged 11-13.5 years) and the United Kingdom (4504 children aged 14-19). We used the Bayesian method for modeling measurement non-invariance proposed by Verhagen and Fox, 2013a that we adapted for using on polytomous items and in a relatively small number of groups (cohorts). Results showed that there is hardly any differential functioning of harmonized anxiety/depression and ADHD scores obtained by CBCL and SDQ across cohorts. The same model that harmonizes measures in Australian 10-year-old children can also be used in cohorts from the UK and the Netherlands. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10862-025-10204-0.