The long-duration fluid physics experiments on a thermocapillary-driven flow have been carried out on the Japanese Experiment Module ‘Kibo’ aboard the International Space Station (ISS) since 2008. In these experiments, various aspects of thermocapillary convection in a half-zone (HZ) liquid bridge of high Prandtl number fluid have been examined under the advantages of the long-duration high-quality microgravity environment. In 2010, the authors succeeded to realize nonlinear convective fields in the HZ liquid bridge of rather high aspect ratio. Special attention was paid on to the complex convective fields, especially on the behaviors of the hydrothermal wave (HTW) over the free surface visualized by an infrared camera. In order to evaluate the characteristics of the nonlinear convective behaviors and their transition processes, the authors indicate the images taken by the infrared camera describing the time evolution of HTW, the spatio-temporal diagram, the Fourier analysis, and the pseudo-phase space, reconstructed from the time series of the scalar information of the liquid bridge, that is, surface temperature variation. In this paper, the authors introduce the signature of complex HTW behaviors observed at the long-duration on-orbit experiments, and make comparisons with some previous terrestrial and microgravity experiments.