Background: Nuclear structure information for the neutron-rich actinide nuclei is important since it is the benchmark for theoretical models that provide predictions for the heaviest nuclei. Purpose: γ -ray spectroscopy of neutron-rich heavy nuclei in the actinide region. Method: Multinucleon-transfer reactions in 70 Zn + 238 U and 136 Xe + 238 U have been measured in two experiments performed at the INFN Legnaro, Italy. In the 70 Zn experiment the high-resolution HPGe Clover Array (CLARA) coupled to the magnetic spectrometer PRISMA was employed. In the 136 Xe experiment the high-resolution Advanced Gamma Tracking Array (AGATA) was used in combination with PRISMA and the Detector Array for Multinucleon Transfer Ejectiles (DANTE). Results: The ground-state band (g.s. band) of 240 U was measured up to the 20 + level and a tentative assignment was made up to the (24 + ) level. Results from γ γ coincidence and from particle coincidence analyses are shown. Moments of inertia (MoI) show a clear upbend. Evidence for an extended first negative-parity band of 240 U is found. Conclusions: A detailed comparison with latest calculations shows best agreement with cranked relativistic Hartree-Bogoliubov (CRHB) calculations for the g.s. band properties. The negative-parity band shows the characteristics of a K π = 0 − band based on an octupole vibration.