Hearing aid device system having a first hearing aid device, wearable on or in the left ear of a user, and having a second hearing aid device, wearable on or in the right ear of a user, wherein each of the two hearing aid devices (HA1, HA2) has a respective directional microphone system and wherein the respective directional microphone system comprises at least - a first microphone (F; F1, F2), which outputs a first microphone signal (SF; SF1, SF2), - a second microphone (B; B1, B2), which outputs a second microphone signal (SB; SB1, SB2), - a delay unit, wherein a directivity is generated by virtue of the second microphone signal (SB; SB1, SB2) or a fourth microphone signal (SB3, SB4) that results therefrom being delayed by an internal time delay (T i; T i 1, T i 2) by means of the delay unit and linked to the first microphone signal (SF; SF1, SF2) or a third microphone signal (SF3, SF4) that results therefrom to generate a directional microphone signal, - a cross-correlation analysis unit (K1, K2), which receives the first (SF; SF1, SF2) or the third (SF3, SF4) microphone signal and the second (SB; SB1, SB2) or the fourth (SB3, SB4) microphone signal, for determining a value of a cross-correlation of the two microphone signals (SF, SB; SF1, SB1, SF3, SB3, SF2, SB2, SF4, SB4), wherein a cross-correlation function of the two microphone signals (SF, SB; SF3, SB3, SF4, SB4) is determinable in the cross-correlation analysis unit (K1, K2) on the basis of a time delay, and wherein an effective time delay (τ eff 1, τ eff 2) is determinable for which the cross-correlation function has a maximum; - a plausibility check unit (P1, P2) for performing a plausibility check for the ascertained effective time delay (τ eff 1, τ eff 2); - a control unit (C1, C2) for adjusting the internal time delay (T i; T i 1, T i 2) on the basis of the value of the cross-correlation of the two microphone signals (SF, SB; SF1, SB1, SF3, SB3, SF2, SB2, SF4, SB4), wherein the adjustable internal time delay (T i; T i 1, T i 2) is the ascertained value of the effective time delay (τ eff 1, τ eff 2) on the basis of the result of the plausibility check; - a classifier to determine a hearing situation that the hearing aid device (HA; HA1, HA2) is currently in, wherein the internal time delay (T i; T i 1, T i 2) is adjusted in particular hearing situations; characterized in that the plausibility check is performable on the basis of a comparison of the effective time delays (τ eff 1, τ eff 2) ascertained in the two hearing aid devices (HA1, HA2). - a first microphone (F; F1, F2), which outputs a first microphone signal (SF; SF1, SF2), - a second microphone (B; B1, B2), which outputs a second microphone signal (SB; SB1, SB2), - a delay unit, wherein a directivity is generated by virtue of the second microphone signal (SB; SB1, SB2) or a fourth microphone signal (SB3, SB4) that results therefrom being delayed by an internal time delay (T i; T i 1, T i 2) by means of the delay unit and linked to the first microphone signal (SF; SF1, SF2) or a third microphone signal (SF3, SF4) that results therefrom to generate a directional microphone signal, - a cross-correlation analysis unit (K1, K2), which receives the first (SF; SF1, SF2) or the third (SF3, SF4) microphone signal and the second (SB; SB1, SB2) or the fourth (SB3, SB4) microphone signal, for determining a value of a cross-correlation of the two microphone signals (SF, SB; SF1, SB1, SF3, SB3, SF2, SB2, SF4, SB4), wherein a cross-correlation function of the two microphone signals (SF, SB; SF3, SB3, SF4, SB4) is determinable in the cross-correlation analysis unit (K1, K2) on the basis of a time delay, and wherein an effective time delay (τ eff 1, τ eff 2) is determinable for which the cross-correlation function has a maximum; - a plausibility check unit (P1, P2) for performing a plausibility check for the ascertained effective time delay (τ eff 1, τ eff 2); - a control unit (C1, C2) for adjusting the internal time delay (T i; T i 1, T i 2) on the basis of the value of the cross-correlation of the two microphone signals (SF, SB; SF1, SB1, SF3, SB3, SF2, SB2, SF4, SB4), wherein the adjustable internal time delay (T i; T i 1, T i 2) is the ascertained value of the effective time delay (τ eff 1, τ eff 2) on the basis of the result of the plausibility check; - a classifier to determine a hearing situation that the hearing aid device (HA; HA1, HA2) is currently in, wherein the internal time delay (T i; T i 1, T i 2) is adjusted in particular hearing situations; characterized in that the plausibility check is performable on the basis of a comparison of the effective time delays (τ eff 1, τ eff 2) ascertained in the two hearing aid devices (HA1, HA2).