The closeness of the evolutionary origin, physiology, and structure of the brain with humans makes lower primates the preferred experimental animals for biomedical research. Many brain diseases induce degradation of cognitive capacities. Various aspects of impairments to cognitive functions are studied in model experiments in monkeys. In the present article we discuss the theoretical grounds for learning complex tasks by primates and present results from training animals using three different behavioral tasks: an oculomotor task, a visual objects categorization task, and a task for assessment of the retention of motor function on extraction of a bait. The results indicate that these tests can be used simultaneously in one animal. This approach leads to optimization of models for studies of cognitive impairments associated with brain diseases.