This study investigates the existence of long-run comovement in the returns of local-currency-denominated bonds of ASEAN-5 countries (Indonesia, Malaysia, the Philippines, Singapore, and Thailand). We explore the pairwise cointegration between Asian local currency bond returns indices using stepwise multiple testing. This helps to identify which pairs of bond indices are cointegrated, while avoiding over-rejection of the null hypothesis or the multiplicity problem. This method is adjusted to deal with possible cross-sectional correlation among the countries. In addition, we assume linear as well as nonlinear models in order to capture potential gradual and asymptotic adjustment of a linear combination of bond indices toward its mean. We find long-term stable relationships among local currency bond returns for some pairs of countries. Specifically, close interlinkages captured as nonlinear cointegration are evident for at least four pairs of countries, namely Indonesia and the Philippines, Malaysia and the Philippines, the Philippines and Thailand, and Singapore and Thailand. In addition, a relatively weak but significant relationship between Malaysia and Thailand is found. Although the adjustment process toward long-run market equilibrium is characterized by the linear model, comovement in bond returns is observed between Malaysia and Singapore.