  Given two conformal field theories related to each other by a marginal
perturbation, and string field theories constructed around such backgrounds, we
show how to construct explicit redefinition of string fields which relate these
two string field theories. The analysis is carried out completely for quadratic
and cubic terms in the action. Although a general proof of existence of field
redefinitions which relate higher point vertices is not given, specific
examples are discussed. Equivalence of string field theories formulated around
two conformal field theories which are not close to each other, but are related
to each other by a series of marginal deformations, is also discussed. The
analysis can also be applied to study the equivalence of different formulation
of string field theories around the same background.
