  We consider the family of all analytic and univalent functions in the unit
disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. Our objective in this paper is
to estimate the difference of the moduli of successive coefficients, that is
$\big | |a_{n+1}|-|a_n|\big |$, for $f$ belonging to the family of
$\gamma$-spirallike functions of order $\alpha$. Our particular results include
the case of starlike and convex functions of order $\alpha$
  and other related class of functions.
