Parameter redundancy was introduced briefly in Section 2.2.2 and encountered in Section 4.3, in the context of the Cormack-Jolly-Seber model for capturerecapture data, and elsewhere. We saw there that two of the model parameters could not be estimated separately, though it was possible to estimate their product. A model with parameters θ is said to be parameter redundant if we can express it in terms of a smaller set of parameters β, so that dim(β) < dim(θ). No amount of data collection can remove parameter redundancy. The deficiency of a parameter-redundant model is d = dim(θ)-dim(β), and models which are not parameter redundant are described as full rank. A model which is full rank for all parameter values is said to be essentially full rank, while a model which is full rank for only a subset of parameter values is said to be conditionally full rank. In this chapter we provide a range of procedures for investigating the parameter redundancy of models. The primary emphases are on the structure of models, and on model-fitting by maximum-likelihood, and the results presented have wide application. In ecology, models are becoming increasingly more complex. It is important to check such models for parameter redundancy, which can be impossible to determine by simple inspection. In addition, numerical optimisation procedures for maximising likelihoods may not identify the consequences of parameter redundancy. We start with two examples to illustrate the basic ideas.