  We extend the Altmann--Mavlyutov construction of homogeneous deformations of
affine toric varieties to the case of toric pairs $(X, \partial X)$, where $X$
is an affine or projective toric variety and $\partial X$ is its toric
boundary. As an application, we generalise a result due to Ilten to the case of
Fano toric pairs.
