A hearing device comprising • a multitude M of input units, each providing an electric hearing device input signal (y 1, y 2), and respective analysis filter banks (FB-A1, FB-A2) for providing each of said electric hearing device input signals (y 1, y 2) in a time-frequency representation Y i (k,m), i=1,..., M, and • a voice activity detection unit (VADU) configured to receive a time-frequency representation Y i (k,m) of at least two electric input signals, i =1,..., M, in a number of frequency bands and a number of time instances, k being a frequency band index, m being a time index, and specific values of k and m defining a specific time-frequency tile of said electric input signals, the electric input signals comprising a target speech signal originating from a target signal source and/or a noise signal, the voice activity detection unit (VADU) being configured to provide a resulting voice activity detection estimate (VA(k,m)) comprising one or more parameters indicative of whether or not a given time-frequency tile contains or to what extent it comprises the target speech signal, and wherein the electric input signals to the voice activity detection unit (VADU) are equal to or originate from said electric hearing device input signals, said voice activity detection unit (VADU) comprises • a first detector (PVAD) for analyzing said time-frequency representation Y i (k,m) of said at least two electric input signals and identifying spectro-spatial characteristics of said electric input signals; and • a second detector (MVAD) for analyzing said time-frequency representation Y i (k,m) of one or more of said at least two electric input signals and identifying spectro-temporal characteristics of said electric input signal(s) Y i (k,m), and providing a preliminary voice activity detection estimate in dependence of said spectro-temporal characteristics; and wherein the voice activity detection unit (VADU) is configured to base the resulting voice activity detection estimate (VA(k,m)) on a combination of said spectro-temporal and said spectro-spatial characteristics, and wherein said preliminary voice activity detection estimate is provided as an input to said first detector (PVAD), and wherein said preliminary voice activity detection estimate comprises a covariance matrix of said at least two electric input signals. • a multitude M of input units, each providing an electric hearing device input signal (y 1, y 2), and respective analysis filter banks (FB-A1, FB-A2) for providing each of said electric hearing device input signals (y 1, y 2) in a time-frequency representation Y i (k,m), i=1,..., M, and • a voice activity detection unit (VADU) configured to receive a time-frequency representation Y i (k,m) of at least two electric input signals, i =1,..., M, in a number of frequency bands and a number of time instances, k being a frequency band index, m being a time index, and specific values of k and m defining a specific time-frequency tile of said electric input signals, the electric input signals comprising a target speech signal originating from a target signal source and/or a noise signal, the voice activity detection unit (VADU) being configured to provide a resulting voice activity detection estimate (VA(k,m)) comprising one or more parameters indicative of whether or not a given time-frequency tile contains or to what extent it comprises the target speech signal, and wherein the electric input signals to the voice activity detection unit (VADU) are equal to or originate from said electric hearing device input signals, said voice activity detection unit (VADU) comprises • a first detector (PVAD) for analyzing said time-frequency representation Y i (k,m) of said at least two electric input signals and identifying spectro-spatial characteristics of said electric input signals; and • a second detector (MVAD) for analyzing said time-frequency representation Y i (k,m) of one or more of said at least two electric input signals and identifying spectro-temporal characteristics of said electric input signal(s) Y i (k,m), and providing a preliminary voice activity detection estimate in dependence of said spectro-temporal characteristics; and