  Transversal oscillations of spicules axes may be related to the propagation
of magnetohydrodynamic waves along them. These waves may become unstable and
the instability can be of the Kelvin-Helmholtz type. We use the dispersion
relation of kink mode derived from linearized magnetohydrodynamic equations.
The input parameters of the derived dispersion equation, namely, spicules and
their ambient medium densities ratios as well as their corresponding magnetic
fields ratios, are considered to be within the range $0-1$. By solving the
dispersion equation numerically, we show that for higher densities and lower
magnetic fields ratios within the range mentioned, the KHI onset in type II
spicules conditions is possible. This possibility decreases with an increase in
Alfven velocity inside spicules. A rough criterion for appearing of
Kelvin-Helmholtz instability is obtained. We also drive a more reliable and
exact criterion for KHI onset of kink waves.
