In this paper, nonlinearity is introduced to linear neural activity decoders to improve continuous hand trajectory prediction for Brain-Computer Interface systems. For decoding the high-dimensional data-tensor, a kernel regression was coupled with multilinear PLS (NPLS). Two ways to introduce nonlinearity were studied: a generalized linear model with kernel link function and kernel regression in the NPLS latent variables space (inside or outside the NPLS iterations). The efficiency of these approaches was tested on the publically available database of the simultaneous recordings of three-dimensional hand trajectories and epidural electrocorticogram (ECoG) signals of a Japanese macaque. Compared to linear methods, nonlinearity did not significantly improve the prediction accuracy but did significantly improve the smoothness of the prediction. © Springer International Publishing AG 2017.