Computational models are becoming more and more the central scientific paradigm for understanding the complexity of living systems. With the increasing number and size of these models there is a growing need for model reuse and exchange. Furthermore, detailed models are not manageable without computer support. There are efforts to formalise the mathematical structure of models (e.g. SBML) and to standardise the kinetic and biological meaning of model components (e.g. SBO, GO, UniProt). However, formalising only the structure of computational models is not sufficient to easily exchange and reuse models and to achieve full computer support for modelling. We also need to formalise the pragmatical and dynamical aspects of models. For this purpose we propose two ontologies: The Kinetic Simulation Algorithm Ontology (KiSAO) and the TErminology for the Description of DYnamics (TEDDY). KiSAO covers algorithms used for simulation of computational models. The ontology classifies and puts into context existing simulation algorithms. For the classification, it uses several criteria such as deterministic/stochastic or spatial/non-spatial. The aim of TEDDY is to provide terms for describing and characterising dynamical behaviours, observable dynamical phenomena, and control elements of biological models and biological systems in Systems Biology and Synthetic Biology.