Complexes of groups are the natural generalizations of graphs of groups. Let \(({\mathcal {G}},{\mathcal {Y}})\) be a developable complex of hyperbolic groups over a finite simplicial complex \({\mathcal {Y}}\) such that the edge groups are finite, and the universal cover of \(({\mathcal {G}},{\mathcal {Y}})\) is a hyperbolic space. In the first part of this note, we describe uniform quasigeodesics in the complex of spaces associated to \(({\mathcal {G}},{\mathcal {Y}})\) . In the second part, we investigate the local quasiconvexity of the fundamental group of certain complexes of locally quasiconvex groups with finite edge groups. Specifically, suppose \({\mathcal {Y}}\) is either a Euclidean polygon with at least four sides or a finite CAT(0) square complex. Consider a complex of groups \(({\mathcal {G}},{\mathcal {Y}})\) in which all the vertex groups are locally quasiconvex and hyperbolic, all the edge groups are finite, and the universal cover of \(({\mathcal {G}},{\mathcal {Y}})\) is a hyperbolic space. We prove that the fundamental group of \(({\mathcal {G}},{\mathcal {Y}})\) is locally quasiconvex if and only if it satisfies the Howson property. Finally, we conclude the paper by discussing relevant applications in the last section.
