  In this work the evolution of two fields of matter in planar symmetric black
holes D-dimensional with symmetry of Lifshitz whose dynamic exponent is $z$
were analyzed. The fields investigated were a scalar field non-minimal coupled
to the Einstein tensor and the Ricci scalar and the electromagnetic field. Two
black holes were chosen, one with 5-dimensions and z=1 and another with
6-dimensions and $z=0$. The equations of motion for both fields were developed
in general and applied to each black hole mentioned. In some cases exact
solutions of the equations were obtained in terms of hypergeometric functions
and confluent Heun functions. The quasinormal modes (MQN) of evolution of the
analyzed fields were calculated numerically using two different approaches: HH
and AIM. In all the black holes studied the NSM's did not indicate
instabilities neither regarding the couplings nor the space-times. In general,
the quasinormal modes behave like the oscillation modes of a damped harmonic
oscillator, presenting three regimes: underdamped $(\omega_R \neq0, \omega_I
<0) $, critically damped $ (\omega_R=0,\omega_I^{crit} <0) $ and overdamped $
(\omega_R=0,\omega_I <0) $. In the analyzed cases an interesting behavior was
found for $\omega_I $ when $ k \neq0 $ and $ r_+<10 $. In general, $\omega_I $
increase with $k$, but here we find a quadratic growth for $ k\sim r_+$ and
then a decrease when $k>>r_+$. This behavior may be relevant in the context of
gravity/gauge duality. Additionally, we also analyzed the evolution of the same
fields in two black holes with symmetry of Lifshtiz in $ 2 + 1 $ dimensions.
