A hearing aid system comprising: a main signal path branch and an active noise cancelling branch, wherein the branches share an acoustical-electrical input transducer, an analog-digital converter, a digital-analog converter, an electrical-acoustical output transducer, a signal splitter configured to branch a signal in the main signal path into the active noise cancelling branch and a signal combiner to add the signals from the two branches; wherein the main signal branch further comprises a digital signal processor configured to apply a frequency dependent gain that is adapted to at least one of suppressing noise and alleviating a hearing deficit of an individual wearing the hearing aid system; and wherein the active noise cancelling branch comprises a group delay reducing element, wherein the group delay reducing element comprises a deconvolution filter configured to have a transfer function that is the inverse of a minimum phase part of a combined transfer function of at least one hearing aid component selected from a group comprising the acoustical-electrical input transducer, the analog-digital converter, the digital-analog converter and the electrical-acoustical output transducer, wherein the output from the analog-digital converter is provided to the signal splitter, whereby the main signal branch and the active noise cancelling branch are formed, and wherein the signal provided from the deconvolution filter is subtracted, using the signal combiner from the signal from the digital signal processor, and wherein the output from the signal combiner is provided to the digital-analog converter and then on to the electrical-acoustical output transducer. a main signal path branch and an active noise cancelling branch, wherein the branches share an acoustical-electrical input transducer, an analog-digital converter, a digital-analog converter, an electrical-acoustical output transducer, a signal splitter configured to branch a signal in the main signal path into the active noise cancelling branch and a signal combiner to add the signals from the two branches; wherein the main signal branch further comprises a digital signal processor configured to apply a frequency dependent gain that is adapted to at least one of suppressing noise and alleviating a hearing deficit of an individual wearing the hearing aid system; and wherein the active noise cancelling branch comprises a group delay reducing element, wherein the group delay reducing element comprises a deconvolution filter configured to have a transfer function that is the inverse of a minimum phase part of a combined transfer function of at least one hearing aid component selected from a group comprising the acoustical-electrical input transducer, the analog-digital converter, the digital-analog converter and the electrical-acoustical output transducer, wherein the output from the analog-digital converter is provided to the signal splitter, whereby the main signal branch and the active noise cancelling branch are formed, and wherein the signal provided from the deconvolution filter is subtracted, using the signal combiner from the signal from the digital signal processor, and wherein the output from the signal combiner is provided to the digital-analog converter and then on to the electrical-acoustical output transducer.