Identifying　causal　relations　among　simultaneously　acquired　signals　is　an　important　challenging　task　in　time　series　analysis.　The　original　definition　of　Granger　causality　was　based　on　linear　models,　its　application　to　nonlinear　systems　may　not　be　appropriate.　We　consider　an　extension　of　Granger　causality　to　nonlinear　bivariate　time　series　with　the　universal　approximation　capacity　in　reproducing　kernel　Hilbert　space　(RKHS)　while　preserving　the　conceptual　simplicity　of　the　linear　model.　In　particular,　we　propose　a　computationally　simple　online　measure　by　means　of　quantized　kernel　least　mean　square　(QKLMS)　to　capture　instantaneous　causal　relationships.