If a,b are n × n matrices, T. Ando proved that Young’s inequality is valid for their singular values: if p > 1 and 1/p + 1/q = 1, then ${\lambda }_k\left(\right|ab*\left|\right)\le {\lambda }_k{(1/p|a|}^p+1/{q\left|b\right|}^q)$ for all k. Later, this result was extended to the singular values of a pair of compact operators acting on a Hilbert space by J. Erlijman, D. R. Farenick and R. Zeng. In this paper we prove that if a,b are compact operators, then equality holds in Young’s inequality if and only if ${\left|a\right|}^p={\left|b\right|}^q$.