Respiratory motion can introduce image artefacts not only in 3D PET but also in 4D PET due to incorrect attenuation correction. In this work the influence of different attenuation correction strategies on 3D and 4D PET has been investigated. An extensive phantom study was carried out, using a normal 3D CT (pitch 1.5), a slow 3D CT (pitch 0.5), an ultraslow 3D CT (pitch 0.15), an average CT and a maximum intensity projection calculated from a 4D CT (pitch 0.1) for attenuation correction of both a 3D and 4D PET of a respiratory motion phantom. Additionally, the 4D PET was corrected phase-wise with a 4D CT (phase-correlated attenuation correction). The reconstructed PET images were analyzed concerning the reconstructed volume, motion amplitude (for 4D PET), activity concentration and activity distribution. Moreover a patient study was carried out investigating the influence of the different attenuation correction strategies for 4D PET to patient data. Therefore 4D PET data from six patients with non-small cell lung cancer (NSCLC) was alternatively attenuation corrected with a normal 3D CT, an average CT and with phase-correlated attenuation correction. The tumor volume was analyzed and the motion amplitude of the tumor was obtained from the 4D PET data sets. For the phantom data the attenuation correction with the slow CT results in the best agreement between expected and measured values of the examined quantities in 3D PET, whereas in 4D PET this was the case for the phase-correlated attenuation correction. In the patient study only small differences between the 4D PET attenuation correction methods were found. This can be explained by the relative small tumor motion in the patient population investigated (peak to peak amplitude below 5 mm except for one patient.