Combining the notions of circular colorings [see \textit{X. Zhu}, Discrete Math. 229, 371--410 (2001; Zbl 0973.05030)] and of list colorings [see \textit{N. Alon} and \textit{M. Tarsi}, Combinatorica 12, 125--134 (1992; Zbl 0756.05049)] in an obvious way the authors introduce circular list colorings of graphs. The corresponding circular list chromatic number \(\chi_{c,l}(G)\) (also called circular choosability) of a graph \(G\) is investigated for outerplanar graphs and for wheels. The results are \(\chi_{c,l}(G)\leq 2+{1\over n}\) for outerplanar graphs \(G\) of girth \(\geq 2n+ 2\) and \(\chi_{c,l}(W_{2k+1})= 4\) for odd wheels.