Sensor device for a motor vehicle, having: evaluation electronics which are designed, for at least one wheel of the motor vehicle: - during a journey of the motor vehicle with a current steering angle (α) below a predefined limit steering angle (α 0) and with an absolute value (|a|) of a current acceleration of the motor vehicle below a predefined limit absolute value (|a 0 |), to determine a multiplicity of first values (ε 1) of a variable representing modulation of a wheel speed (ω) of the respective wheel that is triggered by vibration of a rim of the respective wheel in relation to a wheel hub of the respective wheel, and to determine first amplitudes (A 1) of a first line spectrum of the multiplicity of first values (ε 1) and/or a first variance of the multiplicity of first values (ε 1); - during a journey of the motor vehicle with a current steering angle (α) above the predefined limit steering angle (α 0), wherein the respective wheel is on the inside of a bend of the motor vehicle while the predefined limit steering angle (α 0) is exceeded, and/or with an absolute value (|a|) of a current acceleration of the motor vehicle above the predefined limit absolute value (|a 0 |), to determine a multiplicity of second values (ε 2) of the variable, and to determine second amplitudes (A 2) of a second line spectrum of the multiplicity of second values (ε 2) and/or a second variance of the multiplicity of second values (ε 2); and - to determine, taking into account the first amplitudes (A 1) of the first line spectrum and/or the first variance and taking into account the second amplitudes (A 2) of the second line spectrum and/or the second variance, whether at least one wheel fastening means of the respective wheel has come loose. - during a journey of the motor vehicle with a current steering angle (α) below a predefined limit steering angle (α 0) and with an absolute value (|a|) of a current acceleration of the motor vehicle below a predefined limit absolute value (|a 0 |), to determine a multiplicity of first values (ε 1) of a variable representing modulation of a wheel speed (ω) of the respective wheel that is triggered by vibration of a rim of the respective wheel in relation to a wheel hub of the respective wheel, and to determine first amplitudes (A 1) of a first line spectrum of the multiplicity of first values (ε 1) and/or a first variance of the multiplicity of first values (ε 1); - during a journey of the motor vehicle with a current steering angle (α) above the predefined limit steering angle (α 0), wherein the respective wheel is on the inside of a bend of the motor vehicle while the predefined limit steering angle (α 0) is exceeded, and/or with an absolute value (|a|) of a current acceleration of the motor vehicle above the predefined limit absolute value (|a 0 |), to determine a multiplicity of second values (ε 2) of the variable, and to determine second amplitudes (A 2) of a second line spectrum of the multiplicity of second values (ε 2) and/or a second variance of the multiplicity of second values (ε 2); and - to determine, taking into account the first amplitudes (A 1) of the first line spectrum and/or the first variance and taking into account the second amplitudes (A 2) of the second line spectrum and/or the second variance, whether at least one wheel fastening means of the respective wheel has come loose.