We study the pointwise multipliers in the logarithmic α-Bloch Spaces
and cyclic vectors in the little logarithmic α-Bloch Spaces
. We obtain as follows. (i) A characterization of multipliers on
and
is obtained. (ii) If |f(z)|≥q |g(z)| in the open unit disk and g is cyclic in
, then f is cyclic in
. (iii) If 0<α<1, then f is cyclic in
if and only if f has no zeros in the closed unit disc.