Arterial hypertension is regarded today as a global public health problem, and the prevalence rate in Portugal is 26.9%. According to the etiology, is classified into primary or secondary arterial hypertension. In about 90% of cases it is not possible to establish a cause, so is called primary arterial hypertension. In the remaining 5 to 10%, it can be identified secondary causes, which are potentially treatable. For secondary arterial hypertension study to be cost-effective, it is essential to understand which patients investigate, and evaluate the best strategy to adopt. The main causes identified as responsible for secondary arterial hypertension are: kidney disease; endocrine and vascular diseases and obstructive sleep apnea. Among these some are consensual, and others more controversial in the literature. In this regard we present two cases of arterial hypertension, which are potentially secondary in etiology, but still focus of debate.