In contrast to the traditional approach that uses total mortality rates, we want to gain additional insight into the past development of mortality by concentrating on a more detailed breakdown of mortality data, namely by causes of death. We work with the data from five developed countries (USA, Japan, France, England and Wales, and Australia), two sexes, and split the mortality rates into five main groups of causes of death (Infectious&Parasitic, Cancer, Circulatory diseases, Respiratory diseases, and External causes). As it was shown in Arnold and Sherris (2016), these time series of cause-specific mortality rates are cointegrated and so, there exist long-run equilibrium relationships between them. While the previous research focused on the stationary part of the system of cause-specific mortality rates, in the present paper we study its non-stationary part. For this we explicitly extract common stochastic trends from the original variables and compare them across the different datasets. By testing cointegration assumptions about these trends, we are able to get a better representation and understanding of how cause-specific death rates are evolving. We believe that common patterns emerging from such analysis could indicate a link to more fundamental biological processes such as aging.