MnBi$_4$Te$_{7}$ and MnBi$_6$Te$_{10}$ are two members with n=2 and 3 in the family of MnBi$_{2n}$Te$_{3n+1}$ where the n=1 member, MnBi$_2$Te$_{4}$, has been intensively investigated as the first intrinsic antiferromagnetic topological insulator. Here we report the A-type antiferromagnetic order in these two compounds by measuring magnetic properties, electrical and thermal transport, specific heat, and single crystal neutron diffraction. Both compounds order into an A-type antiferromagnetic structure as does MnBi$_2$Te$_{4}$ with ferromagnetic planes coupled antiferromagnetically along the crystallographic \textit{c} axis. While no evidence for any in-plane ordered moment is found for MnBi$_2$Te$_{4}$ or MnBi$_6$Te$_{10}$, weak reflections at half-L positions along the [0 0 L] direction are observed for MnBi$_4$Te$_{7}$ suggesting an in-plane ordered moment around 0.15$μ_{B}$/Mn. The ordering temperature, T$_N$, is 13\,K for MnBi$_4$Te$_{7}$ and 11\,K for MnBi$_6$Te$_{10}$. The magnetic order is also manifested in the anisotropic magnetic properties. For both compounds, the interlayer coupling is weak and a spin flip transition occurs when a magnetic field of around 1.6\,kOe is applied along the \textit{c}-axis at 2\,K. As observed in MnBi$_2$Te$_4$, when cooling across T$_N$, no anomaly was observed in the temperature dependence of thermopower. On the other hand, critical scattering effects are observed in thermal conductivity although the effect is less pronounced than that in MnBi$_2$Te$_{4}$.