Known is a so-called cross-coupled adaptive noise cancelling arrangement utilizing an adaptive noise filter and an adaptive cross-talk filter in a feedback loop for cancelling correlated noise at a primary signal input and reference input. The known cross-coupled ANC does not operate satisfactorily, particularly not for acoustic noise cancellation. This leads to reverberant-like sound singals, in particular in a typical office room with remote noise sources. A cross-coupled adaptive noise cancelling arrangement is proposed having a different configuration giving rise to a better performance. The adaptive cross-talk filter is split into a prefilter section and an adaptive filter section, the sections using different input signals. The prefilter section estimates the desired signal from the input signal of the noise cancelling arrangement, and the adaptive filter section has its input coupled to the output of the noise cancelling arrangement, a delay section being provided between the input and the output of the noise cancelling arrangement. In an embodiment, the prefilter section and the adaptive filter section are separate filters.