We describe and discuss statistical models of Swedish influenza data, with special focus on aspects which are important in on-line monitoring. Earlier suggested statistical models are reviewed and the possibility of using them to describe the variation in influenza-like illness (ILI) and laboratory diagnoses (LDI) is discussed. Exponential functions were found to work better than earlier suggested models for describing the influenza incidence. However, the parameters of the estimated functions varied considerably between years. For monitoring purposes we need models which focus on stable indicators of the change at the outbreak and at the peak.For outbreak detection we focus on ILI data. Instead of a parametric estimate of the baseline (which could be very uncertain), we suggest a model utilizing the monotonicity property of a rise in the incidence. For ILI data at the outbreak, Poisson distributions can be used as a first approximation.To confirm that the peak has occurred and the decline has started, we focus on LDI data. A Gaussian distribution is a reasonable approximation near the peak. In view of the variability of the shape of the peak, we suggest that a detection system use the monotonicity properties of a peak.