This thesis is devoted to stochastic mortality modelling. The first part considers the popular family of GAPC models and identifies several conceptual difficulties of most well-established models. The GAPC models are embedded in the framework of generalized linear models. However, the vast majority of the literature only considers the canonical link function and by that omits an important modelling factor. In our study, we also incorporate a non-canonical link function and demonstrate its advantages on the fitting performance. While the first part focuses on the static component of the modelling approach, where the main objective is to identify the influencing factors that drive the mortality structure, the second part is devoted to the dynamical part of the modelling approach. For the proposed model we identify appropriate multivariate stochastic processes for the dynamics of the involved stochastic factors. We study cointegration relations between the individual components and compare the forecasting performance with the common GAPC approach. The last part of this thesis can be considered independently of the previous content. There, we provide an extensive characterization of the lifetime distribution which is induced by logistic-type hazard rates of the proposed Kannisto model. Furthermore, we reveal multiple connections to other well-known lifetime distributions.