We have investigated the mean first passage time (MFPT) problem in the presence of a fluctuating barrier. The fluctuation is carried out through colored multiplicative noise. Both Gaussian and non-Gaussian colored noises are considered. Our study shows that the resonant activation (RA) can appear at slower rate of increase of external noise strength with noise correlation time (T) for non-Gaussian noise compared to Gaussian noise. When RA appears for both the noises then minimum in plot of MFPT vs. tau occurs at greater value of tau for Gaussian noise than that for non-Gaussian noise. Our calculation also shows that rate or decrease of the MFPT with increasing strength of additive white noise, is faster for Gaussian colored multiplicative noise compared to corresponding for non-Gaussian case. (c) 2005 Elsevier B.V. All rights reserved.