A graph $G(V,E)$ is $Γ$-harmonious when there is an injection $f$ from $V$ to an Abelian group $Γ$ such that the induced edge labels defined as $w(xy)=f(x)+f(y)$ form a bijection from $E$ to $Γ$. We study $Γ$-harmonious labelings of several cycles-related classes of graphs, including Dutch windmills, generalized prisms, generalized closed and open webs, and superwheels.