Abstract: Let $P$ be a set of $n$ points in $\mathb{R}^3$. The 2-center problem for $P$ is to find two congruent balls of the minimum radius whose union covers $P$. We present two randomized algorithms for computing a 2-center of $P$. The first algorithm runs in $O(n^3\log^8 n)$ expected time, and the second algorithm runs in $O(n^2 \log^{8} n/(1-r^*/r_0)^3)$ expected time, where $r^*$ is the radius of the 2-center of $P$ and $r_0$ is the radius of the smallest enclosing ball of $P$. The second algorithm is faster than the first one as long as $r^*$ is not very close to $r_0$, which is equivalent to the condition of the centers of the two balls in the $2$-center of $P$ not being very close to each other.