The　precipitation　and　growth　morphology　of　topologically　close-packed　(TCP)　phases　in　a　Re-containing　Ni-based　single　crystal　superalloy　during　thermal　exposure　were　studied.　The　alloy　was　found　to　develop　acicular-shaped　coherent　mu　phase　particles　along　＜　110　＞　(gamma)　directions　of　the　matrix　after　exposure　at　950　degrees　C.　P　phase　precipitates　were　found　to　form　with　increased　time　and　at　higher　temperatures,　and　in　different　morphologies,　including　acicular　shaped　particles　along　＜　112　＞　(gamma)　and　＜　110　＞　(gamma)　directions,　and　plate-like　particles　in　{110}(gamma)　planes　of　the　matrix.　The　different　P　phase　precipitates　were　found　to　have　different　lattice　constants　and　different　lattice　correspondences　with　the　matrix.　The　mu　phase　precipitate　was　also　found　to　have　different　lattice　correspondences　with　those　reported　in　the　literature.　The　multiplicity　of　lattice　correspondences　for　the　same　TCP　phase　is　attributed　to　the　different　lattice　parameters,　which　render　the　precipitates　to　have　different　coherency　relationships　with　the　matrix.