Boussinesq and non-Boussinesq gravity currents produced from a finite volume of heavy fluid propagating into an environment of light ambient fluid on unbounded uniform slopes in the range $0\,^\circ \le \theta \le 12\,^\circ$ are reported. The relative density difference $\epsilon = (\rho _1-\rho _0)/\rho _0$ is varied in the range $0.05 \le \epsilon \le 0.15$ in this study, where $\rho _1$ and $\rho _0$ are the densities of the heavy and light ambient fluids, respectively. Our focus is on the influence of the relative density difference on the deceleration phase of the propagation. In the early deceleration phase, the front location history follows the power relationship ${(x_f+x_0)}^2 = {(K_I B)}^{1/2} (t+t_{I})$, where $(x_f+x_0)$ is the front location measured from the virtual origin, $K_I$ an experimental constant, $B$ the total buoyancy, $t$ the time and $t_I$ the $t$ intercept. The dimensionless constant $K_I$ is influenced by the slope angle and the relative density difference. In the late deceleration phase for the gravity currents on the steeper slopes in this study ($12\,^\circ$, $9\,^\circ$ and $6\,^\circ$), an ‘active’ head separates from the body of the current and the front location history follows the power relationship ${(x_f+x_0)}^{8/3} = K_{VS} {B}^{2/3} V^{2/9}_0 {\nu }^{-1/3} ({t+t_{VS}})$, where $K_{VS}$ is an experimental constant, $V_0$ the total volume of heavy fluid, $\nu$ the kinematic viscosity of fluid and $t_{VS}$ the $t$ intercept. The dimensionless constant $K_{VS}$ is shown to be influenced by the slope angle but not significantly influenced by the relative density difference. In the late deceleration phase for the gravity currents on the milder slopes in this study ($3\,^\circ$ and $0\,^\circ$), the gravity currents maintain an integrated shape without violent mixing with the ambient fluid and the front location history follows the power relationship ${(x_f+x_0)}^{4} = K_{VM} {B}^{2/3} V^{2/3}_0 {\nu }^{-1/3} ({t+t_{VM}})$, where $K_{VM}$ is an experimental constant and $t_{VM}$ the $t$ intercept. The dimensionless constant $K_{VM}$ is shown to be influenced by both the slope angle and the relative density difference. While the influence of the relative density difference on $K_{VM}$ is carried along for the gravity currents on the milder slopes in the late deceleration phase, the relative density difference interestingly has no significant influence on $K_{VS}$ for the gravity currents on the steeper slopes in the late deceleration phase. Our results suggest that the non-Boussinesq gravity currents on the milder slopes may remain non-Boussinesq ones in the late deceleration phase while the non-Boussinesq gravity currents on the steeper slopes may have become Boussinesq ones in the late deceleration phase.