We investigate the photoluminescence of interlayer excitons in heterostructures consisting of monolayer MoSe2 and WSe2 at low temperatures. Surprisingly, we find a doublet structure for such interlayer excitons. Both peaks exhibit long photoluminescence lifetimes of several ten nanoseconds up to 100 ns at low temperatures, which verifies the interlayer nature of both.The peak energy and linewidth of both show unusual temperature and power dependences.In particular, we observe a blue-shift of their emission energy for increasing excitation powers.At a low excitation power and low temperatures, the energetically higher peak shows several spikes. We explain the findings by two sorts of interlayer excitons; one that is indirect in real space but direct in reciprocal space, and the other one being indirect in both spaces. Our results provide fundamental insights into long-lived interlayer states in van der Waals heterostructures with possible bosonic many-body interactions.Keywords: van der Waals heterostructure, indirect excitons, interlayer exciton, photoluminescence, exciton lifetime, transition metal dichalcogenides; 2 Semiconductor heterostructures (HS) are very often the foundation for the observation of novel phenomena in both fundamental science as well as device applications. The electrical and optical properties of such HS can be engineered in a wide range resulting in precisely tailored functionalities. Of particular interest are optically active HS facilitating many device applications such as photo-detectors, solar cells, light-emitting diodes or lasers and fostering the observation of many-body driven quantum phenomena found in systems with reduced dimensionality such as quantum wells or quantum dots. Excitons are electron-hole pairs coupled by attractive Coulomb interaction which results in a ground state with a reduced energy compared to the corresponding single-particle energies. Exciton ensembles exhibit an intriguing interaction driven phase diagram with different classical and quantum phases including quantum liquids and solids [1][2][3]. The bosonic nature of excitons enables these composite particles even to condensate into macroscopic ground state wave functions forming a Bose-Einstein condensate (BEC) [4].Ensembles of indirect a.k.a. interlayer excitons (IXs) are particularly fascinating systems to explore such classical and quantum phases of interacting bosonic ensembles. IXs are composite bosons that feature enlarged lifetimes due to the reduced overlap of the electronhole wave functions resulting in dense IX ensembles that are thermalized to the lattice temperature. Besides IX ensembles in III-V HS [5][6][7][8][9][10][11][12][13][14][15], hetero-bilayers prepared from semiconducting transition metal dichalcogenides (TMDs) exhibit superior potential for studying interacting IX ensembles [3,[16][17][18][19][20][21][22][23][24][25] with intriguing spin-and valley-properties [26][27][28]. At the same time, TMDs are truly two-dimensional (2D) crystals coupled to each other or to substrat...