This paper provides new evidence on the impacts of financial constraints, growth opportunities and debt overhang on firm-level investments in 12 Asian countries, Australia and New Zealand over the period 1990–2010. Using Panel Smooth Transition Regression (PSTR) models that overcome the shortcomings of linear investment models, we show that the PSTR models have greater explanatory power than linear models. The empirical results show that for firms with growth opportunities, (1) investment is sensitive to the availability of internal finance and (2) debt overhang reduces investment by firms with higher leverage through a 'liquidity' effect. Our findings imply that the managers of financially constrained firms in developed countries in the Asian region respond differently to productivity shocks and growth opportunities than financially constrained firms in emerging markets and developing countries. In addition, in emerging Asian economies, higher equity valuations increased firm-level investment after the stock markets opened to foreign investors. Accordingly, policy makers should review their liberalisation measures and seek to understand the mechanisms at work in order to bolster international investors' confidence and stimulate foreign investment.