  We deal with hypersurfaces in the framework of the relative differential
geometry in $\mathbb{R}^4$. We consider a hypersurface $\varPhi$ in
$\mathbb{R}^4$ with position vector field $\vect{x}$ which is relatively
normalized by a relative normalization $\vect{y}$. Then $\vect{y}$ is also a
relative normalization of every member of the one-parameter family
$\mathcal{F}$ of hypersurfaces $\varPhi_\mu$ with position vector field
$\vect{x}_\mu = \vect{x} + \mu \, \vect{y}$, where $\mu$ is a real constant. We
call every hypersurface $\varPhi_\mu \in \mathcal{F}$ relatively parallel to
$\varPhi$. This consideration includes both Euclidean and Blaschke
hypersurfaces of the affine differential geometry. In this paper we express the
relative mean curvature's functions of a hypersurface $\varPhi_\mu$ relatively
parallel to $\varPhi$ by means of the ones of $\varPhi$ and the "relative
distance" $\mu$. Then we prove several Bonnet's type theorems. More precisely,
we show that if two relative mean curvature's functions of $\varPhi$ are
constant, then there exists at least one relatively parallel hypersurface with
a constant relative mean curvature's function.
