It is well-known that if one or a few components in a structure are of nonlinear properties, the whole structure will behave nonlinearly, and the nonlinear component is often the component where a fault or an abnormal condition occurs. Therefore it is of great significance to detect the position of nonlinear components in structures. Nonlinear output frequency response functions (NOFRFs) are a new concept proposed by the authors for the analysis of nonlinear systems in the frequency domain. The present study is concerned with investigating the NOFRFs of nonlinear one-dimensional chain type systems, which have been widely used to model many real life structures. A series of important properties of the NOFRFs of locally nonlinear one-dimensional chain type structures are revealed. These properties clearly describe the relationships between the NOFRFs of different masses in a one-dimensional chain type system, and allow effective methods to be developed for detecting the position of a nonlinear component in the system. The results are an extension of the authors’ previous research studies to a more general and practical case, and have considerable significance in fault diagnosis and location in engineering systems and structures.