Background and Objectives: Posttraumatic stress disorder (PTSD) caused by war trauma experiences affects veterans’ ability to meet their parental obligations, which can lead to the appearance of psychological and behavioral problems in their children. We explored, based on the parents’ assessment, whether the children of veterans with PTSD exhibit more psychological and behavioral problems and whether there are differences in relation to the age and sex of the child. Methods: The study group consisted of 91 children from 50 veterans receiving treatment for the war-related PTSD at the Psychiatric Department of the University Clinical Hospital Mostar. The control group consisted of 98 children of 50 war veterans without PTSD who were selected from veteran associations by the snowball method. The following instruments were used in the study: General Demographic Questionnaire, Harvard Trauma Questionnaire-Bosnia and Herzegovina version and the Strengths and Difficulties Questionnaire for children. Results: Children of veterans with PTSD have more pronounced psychological and behavioral problems (U = 2372.5; P < 0.001) compared to the children of veterans without PTSD. Male children of veterans with PTSD have more frequent behavioral problems (chi2 = 7.174; P = 0.025) compared to the female children, and overall, they more frequently exhibit borderline or abnormal psychological difficulties (chi2 = 6.682; P = 0.029). Children exhibiting abnormal levels of hyperactivity are significantly younger than children who exhibit normal or borderline levels of hyperactivity (Kruskal-Wallis = 3.982; P = 0.046). Conclusions: The children of war veterans with PTSD have more psychological and behavioral problems in comparison with the children of veterans without PTSD.