Background: Many nuclear-structure features have been observed in the actinides during the last decades. Especially the octupole degree of freedom has been discussed lately after the successful measurement of the B E3; 0 + 1 → 3 − 1 reduced transition strength in 224 Ra. Recent results stemming from γ-spectroscopy experiments and high-resolution (p, t) experiments suggested, that strong octupole correlations might be observed for some positive-parity states of actinide nuclei. Purpose: This work completes a series of (p, t) experiments on actinide nuclei by adding the data on 240 Pu. The (p, t) experiments allow to study low-spin states up to J π = 6 + . Besides two-nucleon transfer cross sections, spin and parity can be assigned to excited states by measuring angular distributions, and several rotational bands are recognized based on these assignments. Methods: A high-resolution (p,t) experiment at Ep= 24 MeV was performed to populate lowspin states in the actinide nucleus 240 Pu. The Q3D magnetic spectrograph of the Maier-Leibnitz Laboratory (MLL) in Munich (Germany) was used to identify the ejected tritons via dE/E particle identification with its focal-plane detection system. Angular distributions were measured at nine different Q3D angles to assign spin and parity to the excited states based on a comparison with coupled-channels DWBA calculations. Results: In total, 209 states have been excited in 240 Pu up to an excitation energy of 3 MeV. Many previously known states have also been observed and their spin-parity assignments were confirmed. However, many of the populated states have been seen for the first time, e.g., 15 new and firmly assigned J π = 0 + states. In addition, all low-spin one-octupole phonon excitations, i.e. K π = 0 − , 1 − , 2 − , 3 − , could be observed and a new candidate for the K = 3 projection is proposed. Furthermore, the double-octupole or α-cluster structure of the 0 + 2 state in 240 Pu has been studied in more detail. It is shown that the 0 + 2 state in 230 Th has a distinctly different structure. In addition, strongly excited 1 − states have been observed at 1.5 MeV and 1.8 MeV in 240 Pu. The present study suggests that similar states might be observed in 230 Th. Conclusions: At least two different and distinct structures for J π = 0 + states are present in the actinides. These are pairing states and states with enhanced octupole correlations. We have shown that it is crucial to consider negative-parity single-particle states being admixed to some K π = 0 + 2 rotational bands to understand the α-decay hindrance factors and enhanced E1-decay rates. Based on our analysis, we have identified the double-octupole or α-cluster K π = 0 + candidates from 224 Ra to 240 Pu.