Summary: Graphical methods based on the analysis of residuals are considered for the setting of the highly-used D. R. Cox [J. R. Stat. Soc., Ser. B 34, 187-220 (1972; Zbl 0243.62041)] regression model and for the P. K. Andersen and R. D. Gill [Ann. Stat. 10, 1100-1120 (1982; Zbl 0526.62026)] generalization of that model. We start with a class of martingale-based residuals as proposed by W. E. Barlow and R. L. Prentice [Biometrika 75, 65-74 (1988; Zbl 0632.62102)]. These residuals and/or their transforms are useful for investigating the functional form of covariate, the proportional hazards assumption, the leverage of each subject upon the estimates of \(\beta\), and the lack of model fit to a given subject.