  Quasinormal modes of massless test scalar field in the background of
gravitational field for a non-extremal dilatonic dyonic black hole are
explored. The dyon-like black hole solution is considered in the gravitational
$4d$ model involving two scalar fields and two 2-forms. It is governed by two
2-dimensional dilatonic coupling vectors $\vec{\lambda}_i$ obeying
$\vec{\lambda}_i (\vec{\lambda}_1 + \vec{\lambda}_2) > 0$, $i =1,2$.
Quasinormal modes for a massless scalar (test) field in the eikonal
approximation are obtained and analysed. These modes depend upon a
dimensionless parameter $a$ ($0 < a \leq 2$) which is a function of
$\vec{\lambda}_i$. For limiting strong ($a = +0$) and weak ($a = 2$) coupling
cases, they coincide with the well-known results for the Schwarzschild and
Reissner-Nordstr\"om solutions. It is shown that the Hod conjecture, connecting
the damping rate and the Hawking temperature, is satisfied for $0 < a \leq 1$
and all allowed values of parameters.
