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A matrix $𝒜$ whose entries come from the set $\{+,-,0\}$ is called a , or . A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, the characterization problem for some potentially nilpotent double star sign patterns is discussed. A class of double star sign patterns, denoted by $𝒟SSP(m,2)$, is introduced. We determine all potentially nilpotent sign patterns in $𝒟SSP(3,2)$ and $𝒟SSP(5,2)$, and prove that one sign pattern in $𝒟SSP(3,2)$ is potentially stable.