The evolution of rapid solidification (RS) microstructure and solidification interface velocity has been studied experimentally by in-situ transmission electron microscopy and postmortem characterization for hypereutectic Al-20at.%Cu (37 wt.%Cu) after laser melting. Four morphologically distinct regions formed via growth modes changing from θ-Al2Cu phase dendrites to eutectic cell growth, possibly α-Al dendrite growth (α-cell), banded growth, and α-Al plane front growth. Tendency for faceting and low capacity for solute trapping limited the θ-phase dendrite growth to solidification interface velocity v < 0.07 m/s. Consequently, formation of pro-eutectic micro-constituent was suppressed, and RS microstructure formation was dominated by eutectic, α-cell, and banded morphology grains for the Al-20at.%Cu alloy. Eutectic growth operated for interface velocity of 0.1 m/s ≤ v < 0.3 m/s, with a transition from regular lamellar, 2-λ and 1-λ mode to a dense irregular morphology dominated by α-phase at v = 0.3 m/s. Interface temperature calculations indicated feasibility of α-cell growth mode for 0.3 m/s ≤ v < 0.7 m/s. Banded growth occurred for 0.7 m/s ≤ v < 1.3 m/s. Plane front α-phase growth was evident for interface velocities v ≥ 1.3 m/s. Previous work on rapid solidification microstructure development in hypereutectic Al-Cu alloys reported a regime of α-cell growth subsequently to eutectic and prior to transition to banded growth for Al-19at.%Cu (36 wt.%Cu), while for Al-22at.%Cu (40 wt.%Cu) eutectic growth transitioned directly to α-plane front growth without emergence of a banded regime. Based on the current study the disappearance of the banded growth regime occurs for a composition larger than 20at.%Cu.