A　self-consistent　rate　equations　method　is　applied　to　investigate　the　nucleation　process　in　the　early　stage　of　SiC　(0001)　surface　epitaxial　growth.　Si-Si,　C–C　and　Si-C　are　considered　to　be　unstable　dimers　and　the　dissociation　rates　are　determined　by　their　binding　energies,　substrate　temperature　and　the　geometry　of　adsorption　sites　of　Si　and　C　on　the　surface.　The　time　evolution　of　monomer,　dimer　and　stable　cluster　density　as　well　as　their　dependences　on　temperature　are　in　good　agreement　with　KMC　simulation　results.　A　transition　zone　in　the　profiles　of　stable　cluster　density　for　different　temperatures　is　observed,　and　this　is　caused　by　the　effect　of　temperature　on　net　nucleation　rate　of　dimer,　which　will　determine　the　number　of　cores　for　stable　cluster.　Si-Si　dimer　can　hardly　exist　due　to　its　much　smaller　binding　energy.　The　formation　of　Si-C　is　prior　to　the　formation　of　C–C　dimer,　which　indicates　that　the　stable　clusters　are　mainly　formed　by　the　Si-C　nucleation　until　the　density　of　C–C　is　higher　than　that　of　Si-C　dimer.　Furthermore,　for　higher　coverage,　the　density　of　dimer　decreases　with　the　increase　of　temperature,　leading　to　the　smaller　saturation　value　of　stable　clusters　density　at　higher　temperature.　©　2020　Elsevier　B.V.