This study addresses the fault detection problem in multimode processes containing linear and nonlinear relations. The continued-improved partial least squares-improved kernel partial least squares (C-IPLS-IKPLS) model is first proposed and then the designed model is integrated into an external analysis framework. The specific concepts of the C-IPLS-IKPLS model are as follows: (1) IPLS, in which data are divided into two mutually orthogonal parts, is first employed to extract all linear-related information; (2) the residual information is further analyzed using IKPLS to extract all nonlinear-related information. To achieve the optimal fault detection effect for multimode processes, a C-IPLS-IKPLS-based external analysis model is constructed, which not only considers all linear and nonlinear relations but also completely discriminates the final detection information. Finally, the proposed method's effectiveness is verified by applying it to a numerical example and the Pensim benchmark process. The results demonstrate that the proposed method can effectively and accurately detect faults in multimode processes that feature linear and nonlinear relations.