In this article, we examine whether per-capita health expenditures and per-capita GDP for 11 OECD countries can be characterized by asymmetric behaviour. We achieve this goal by using the nonparametric Triples test suggested by Randles et al. (1980). We examine two forms of asymmetries, namely deepness and steepness. Our main finding is that for 6 out of 11 countries, namely for the USA, the UK, Japan, Spain, Finland and Iceland, either per-capita health expenditures or per-capita GDP are characterized by asymmetric behaviour. This finding to some extent casts doubt on those studies that model the relationship between health and GDP using unit-root and cointegration tests that assume symmetric disturbances.