The ordinary at $m=1$ and the completely solvable at $m>1$ the real homogeneous Darboux systems $$dx_i=\sum\limits_{j=1}^{m}\Bigl(L_{ij}(x)+x_iP_j(x) \Bigr)dt_j, i=\overline{1,n},$$ where $n>1,\ m<n,\ L_{ij}(x)=\sum\limits_{k=1}^{n}a_{ijk}x_k,\ a_{ijk}\in\mathbb{R},\ k=\overline{1,n},\ j=\overline{1,m},\ i=\overline{1,n},\ P_j(x),\ j=\overline{1,m}$, are twice smooth homogeneous functions of order $\rho\geqslant 1$ and the rank of the matrix corresponding to the right-hand sides of the Darboux systems is equal to m almost everywhere on $\mathbb{R}^n$, are considered. The concept of a regular integral hypersurface of these systems is introduced. It is proved that the systems under consideration cannot have more than one isolated compact regular integral hypersurface. An example of a system with an isolated compact regular integral hypersurface is given.