In this paper, we give definitions and characterizations of slant helices, normalized Darboux helices and similar curves in dual space $\mathbb{D}^{3}$. First, we define dual slant helices and dual normalized Darboux helices and show that dual slant helices are also dual normalized Darboux helices. Then, we introduce the concept of dual similar curves and obtain that the family of dual slant helices forms a family of dual similar curves.