Several mathematical models have been developed to describe the composting process. The degradation rate of the substrate is an important criterion to determine the effectiveness of the process and to design optimization strategies in composting. Kinetic models’ development plays an important role in composting process management. The aim of this research was to estimate the kinetic parameters and to develop a kinetic model on the degradation process of organic fraction of municipal solid waste (OFMSW) separated at source in two independent composting facilities located in rural areas near to the city of Medellín (Colombia). The composts obtained showed adequate physical-chemical properties. Existent models based on first-order kinetics were selected and new values of model parameters were found by a nonlinear fitting procedure. The kinetic models of the composting of OFMSW included process parameters such as electric conductivity (EC), temperature and oxygen concentration. The developed model has been adjusted with experimental data obtained from two composting facilities located in different environmental conditions, which allowed a good prediction of the degradation rate of organic matter (OM). Kinetic models and data analysis proposed allowed a better understanding of transformation processes of OM during municipal solid waste composting in areas under tropical climate. The developed analysis could be used as a tool for composting simulation and optimization of process parameters.