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Score-driven models, also known as generalized autoregressive score models, represent a class of observation-driven time series models. They possess powerful properties, such as the ability to model different conditional distributions and to consider time-varying parameters within a flexible framework. In this paper, we present ScoreDrivenModels.jl, an open-source Julia package for modeling, forecasting, and simulating time series using the framework of score-driven models. The package is flexible with respect to model definition, allowing the user to specify the lag structure and which parameters are time-varying or constant. It is also possible to consider several distributions, including Beta, Exponential, Gamma, Lognormal, Normal, Poisson, Student's t, and Weibull. The provided interface is flexible, allowing interested users to implement any desired distribution and parametrization.