Combustion of industrial gases has gained increasing attention in the past decades. Great challenges for reliable industrial operation are posed by combustion instability. In this study, the oscillating combustion of industrial gases are classified into four typical types according to different causes for the first time. Typical causes of oscillating combustion include intrinsic mixing/kinetics/heat loss interaction, single inflowing fluctuation, inflowing fluctuation superposition and fuel switching. All the four typical oscillating combustion have been systematically analyzed with the unsteady perfectly stirred reactor combustion model and chemical explosive mode analysis. The physical reasons for typical combustion stabilities have been further revealed with the kinetic importance of dependent variable and chemical reaction. The short-term and long-term prediction models have been established within a wide range of system parameters using the generalized functional form of NARMAX and neural network method. The short-term prediction model aims to predict the short-term local physical information, and the long-term prediction model, which uses the clustered prediction method, aims to be a general prediction model for all the four typical types to meet the requirement of existing combustion instability controller. These prediction models making full use of the robustness of neural networks for nonlinear functions provide validation and data support for the design of controller and actuator.