  The structural and the magnetic properties of CeCu$_{6-x}$Ag$_x$ (0 $\leq$
$x$ $\leq$ 0.85) and CeCu$_{6-x}$Pd$_x$ (0 $\leq$ $x$ $\leq$ 0.4) have been
studied using neutron diffraction, resonant ultrasound spectroscopy (RUS), heat
capacity, x-ray diffraction measurements and first principles calculations. The
structural and magnetic phase diagrams of CeCu$_{6-x}$Ag$_x$ and
CeCu$_{6-x}$Pd$_x$ as a function of Ag/Pd composition are reported. The end
member, CeCu$_6$, undergoes a structural phase transition from an orthorhombic
($Pnma$) to a monoclinic ($P2_1/c$) phase at 240 K. In CeCu$_{6-x}$Ag$_x$, the
structural phase transition temperature (${T_{s}}$) decreases linearly with Ag
concentration and extrapolates to zero at $x_{S}$ $\approx$ 0.1. The structural
transition in CeCu$_{6-x}$Pd$_x$ remains unperturbed with Pd substitution
within the range of our study. The lattice constant $b$ slightly decreases with
Ag/Pd doping, whereas, $a$ and $c$ increase with an overall increase in the
unit cell volume. Both systems, CeCu$_{6-x}$Ag$_x$ and CeCu$_{6-x}$Pd$_x$,
exhibit a magnetic quantum critical point (QCP), at $x$ $\approx$ 0.2 and $x$
$\approx$ 0.05 respectively. Near the QCP, long range antiferromagnetic
ordering takes place at an incommensurate wave vector ($\delta_1$ 0 $\delta_2$)
where $\delta_1 \sim 0.62$, $\delta_2 \sim 0.25$, $x$ = 0.125 for
CeCu$_{6-x}$Pd$_x$ and $\delta_1 \sim 0.64$, $\delta_2 \sim 0.3$, $x$ = 0.3 for
CeCu$_{6-x}$Ag$_x$. The magnetic structure consists of an amplitude modulation
of the Ce-moments which are aligned along the $c$-axis of the orthorhombic unit
cell.
