Part I of this paper [17] developed and verified the numerical model for simultaneous heat and moisture transfer in the run-around membrane energy exchanger (RAMEE) system to determine the transient behavior of the system under different initial and operating conditions. This paper presents the transient response of the RAMEE system for step changes in the inlet supply air temperature and humidity ratio. Also the system quasi-steady state operating conditions are predicted as the system approaches its asymptotic operating condition. The transient responses are predicted with changes in various parameters. These include: the number of heat transfer units, thermal capacity ratio, heat loss/gain ratio, storage volume ratio and the normalized initial salt solution concentration. It is shown that the storage volume ratio and the initial salt solution concentration have significant impacts on the transient response of the system and heat transfer between the RAMEE system and the surrounding environment can change the system quasi-steady conditions substantially. (C) 2009 Elsevier Ltd. All rights reserved.