The Holt-Winters models are one of the most popular forecasting algorithms. As well-known, these models are recursive and thus, an initialization value is needed to feed the model, being that a proper initialization of the Holt-Winters models is crucial for obtaining a good accuracy of the predictions. Moreover, the introduction of multiple seasonal Holt-Winters models requires a new development of methods for seed initialization and obtaining initial values. This work proposes new initialization methods based on the adaptation of the traditional methods developed for a single seasonality in order to include multiple seasonalities. Thus, new methods to initialize the level, trend, and seasonality in multiple seasonal Holt-Winters models are presented. These new methods are tested with an application for electricity demand in Spain and analyzed for their impact on the accuracy of forecasts. As a consequence of the analysis carried out, which initialization method to use for the level, trend, and seasonality in multiple seasonal Holt-Winters models with an additive and multiplicative trend is provided.