Several diagnostics have been proposed to detect observations which exert substantial influence on the estimation of regression coefficients in generalized linear models. Instead of the well-known approach to define a one-step estimate of the change in the regression coefficients a local influence method to assess the effect of small perturbations of the data is applied in this paper. The latter method includes perturbations in the vector of responses, case weights, explanatory variables, and the components of one case. The resulting diagnostic allows one to check for different kinds of influence. Two examples illustrate the method.