Time-dependent models of the form $Y_t := f(\mathbf{X}, t)$ ($t \in [0, T]$, $\mathbf{X} \in \mathbb{R}^d$) are widely used and developed in science and engineering, and such computational models are sometimes evaluated at non-independent variables, such as correlated or/and dependent variables. Non-independent variables arise when at least two variables cannot vary freely, and the corresponding dependency structures impact the inputs effects, such as generalized sensitivity indices (GSIs [1-3]), including Sobol' indices, so that GSIs fail of being a dependent measure of association between dependent inputs and dynamic outputs in general. While extended GSIs provided in [4-5] remain a valid dependent measure, there are some interpretability issues. This study proposes dependent generalized sensitivity indices (DGSIs) by making use of equivalent representations of time-dependent models. Composing models by dependency models of non-independent variables ([4-6]) yields equivalent representations. The proposed DGSIs are the percentages of the outputs variability due to every input and interactions. Thus, the first-order DGSI is always less than the total one, and the total DGSIs serve as a dependent measure of association between non-independent inputs and dynamic outputs. Such DGSIs allow for extending i) dependent sensitivity indices from [7], and ii) the Shapley effects ([8-9]) for vector-valued models with Gaussian random vector.