Abstract Higher order statistics and Wigner higher order moment spectra were used to extract useful flow regime characteristics from wall pressure fluctuation signals in an annulus sparged internal loop airlift reactor. It is found that the pressure fluctuation in the airlift reactor is a typical nonlinear and non-stationary process, which exhibits different frequency characteristics depending on flow regimes. Analysis methods based on bispectrum and Wigner trispectrum are powerful tools to reveal frequency characteristics of pressure signals. To identify flow regime transitions in the reactor, two new characteristic quantities, namely average bispectrum and generalized average frequency, are defined from bispectrum and Wigner trispectrum of the pressure signal, respectively. Two flow regime transition points corresponding to three flow regimes in the reactor are successfully detected by using these two characteristic quantities.