This thesis contributes to influence analysis in nonlinear regression and in particular the detection of influential observations. The focus is on a regression model with a known mean function, which is nonlinear in its parameters and where the function is chosen according to the knowledge about the process generating the data. The error term in the regression model is assumed to be additive. The main goal of this thesis is to work out diagnostic measures for assessing the influence of observations on various results from a nonlinear regression analysis. The obtained results comprise diagnostic tools for detecting observations that, individually or jointly with some other observations, are influential on the parameter estimates. Moreover, assessing conditional influence, i.e. the influence of an observation conditional on the deletion of another observation, is of interest. This can help to identify influential observations which could be missed due to complex relationships among the observations. Novelties of the proposed diagnostic tools include the possibility to assess influence of observations on a specific parameter estimate and to assess influence of multiple observations. A further emphasis of this thesis is on the observations' influence on the outcome of a hypothesis testing procedure based on Rao's score test. An innovative solution to the problem of visual identification of influential observations regarding the score test statistic obtained in this thesis is the so called added parameter plot. As a complement to the added parameter plot, new diagnostic measures are derived for assessing the influence of single and multiple observations on the score test statistic.