Many medical and biological studies involve response in the form of Poisson counts which can bemodelled using explanatory variables which also arise from count data. If the explanatory variables are observable without error (also as Poisson counts) we have a generalized linear model with a logarithmic link function and Poisson error structure. If,however, some of the explanatory variables are not directly observable, but arise with superimposed errors (again of Poisson form), the model is of a new type:a generalised linear functional Poisson model. In this paper,maximum likelihood estimates of the parameters of this model are determined along with the information matrix which (on noting its particular patterned form) is amenable to inversion in explicit form. Methods are proposed of an iterative type for computing estimates of the parameters and of their variational properties (e.g. standard errors) for this model, which also has application in other fields such as road traffic studies.