The operational modal analysis methods based on output-only measurements are well-known and applied in linear systems. However, they are not so well developed for nonlinear systems. Thus, this paper proposes an approach for nonlinear system identification using output-only data. In the conventional Volterra series, the outputs of the system are computed by multiple convolutions between the excitation force and the Volterra kernels. However, in this paper at least two time series measured in different placements are used to compute the multiple convolutions and the excitation signals are not required. The novel kernels identified can be used to characterize nonlinear behavior through a model using only output data. A numerical example based on a Duffing oscillator with two degrees-of-freedom (2DOF) and experimental vibration data from a buckled beam with hardening nonlinearities are used to illustrate the proposed method. The prediction results using output-only data are similar to the conventional Volterra kernels based on input and output data.