A combination of scanning electron microscopy (SEM), transmission electron microscopy (TEM) and scanning-transmission electron microscopy (STEM) using high-angle annular-dark-field (HAADF) imaging, focussed ion beam- scanning electron microscopy (FIB-SEM) tomography, selected area electron diffraction with beam precession (PED), as well as spatially resolved energy-dispersive X-ray spectroscopy (EDS) and electron energy loss spectroscopy (EELS), was used to investigate topologically close-packed (TCP) phases, occurring in the CMSX-4 superalloy subjected to high temperature annealing and creep deformation. Structural and chemical analyses were performed to identify the TCP phases and provide information concerning the compositional partitioning of elements between them. The results of SEM and FIB-SEM tomography revealed the presence of merged TCP particles, which were identified by TEM and PED analysis as coprecipitates of the μ and P phases. Inside the TCP particles that were several micrometres in size, platelets of alternating μ and P phases of nanometric width were found. The combination of STEM-HAADF imaging with spatially resolved EDS and EELS microanalysis allowed determination of the significant partitioning of the constituent elements between the μ and P phases.