  We present an extensive study of the structural, magnetic and thermodynamic
properties of high-quality monocrystals of the two heterometallic oxyborates
from the ludwigite family: Cu$_2$GaBO$_5$ and Cu$_2$AlBO$_5$ in the temperature
range above 2 K. The distinctive feature of the investigated structures is the
selective distribution of Cu and Ga/Al cations. The unit cell of Cu$_2$GaBO$_5$
and Cu$_2$AlBO$_5$ contains four nonequivalent crystallographic sites of metal
ions. Two sites in the structure from four nonequivalent crystallographic sites
of metal ions of Cu$_2$GaBO$_5$ are fully occupied by Cu atoms which form the
quasi one-dimensional chains along the a-axis. For Cu$_2$AlBO$_5$ all sites are
partially occupied by Al and Cu atoms. The joint analysis of low-temperature
data on magnetic susceptibility and magnetic contribution to the specific heat
showed that Cu$_2$AlBO$_5$ and Cu$_2$GaBO$_5$ exhibit an antiferromagnetic
transition at $T_{\rm N} \approx 3$ and 4 K, respectively. The magnetic
contributions to the specific heat for both compounds were obtained after
subtracting the phonon contribution. It is shown that the external magnetic
field above 2.5 T leads to a broadening of the magnetic phase transition
indicating suppression of the long-range antiferromagnetic order.
