This invention relates to a dual phase rubber composition and pneumatic tire with a rubber sidewall thereof, namely a dual phased non-black colored rubber composition composed of a first pre-formed elastomer phase comprised of butyl-type rubber and EPDM rubber containing a dispersion therein of reinforcing filler comprised of a particulate amorphous precipitated silica and a second pre-formed elastomer phase comprised of a nanocomposite of natural rubber containing a dispersion therein of exfoliated clay platelets. Said exfoliated clay platelets may be substantially oriented within the tire sidewall in a parallel direction to each and may also be substantially oriented in an annular direction about the axis of the tire. The tire sidewall rubber composition may contain at least one additional elastomer which may be included in either or both of said elastomer phases. Such tire sidewall rubber composition may contain a non-black colorant pigment, such as for example a white colored titanium dioxide pigment. The dual phased tire sidewall rubber composition is prepared by a phase mixing process comprised of pre-blending said butyl-type rubber and EPDM rubber together with said precipitated silica reinforcing filler to form a pre-mix thereof, and thereafter mixing therewith said nanocomposite as a pre-formed blend of natural rubber and exfoliated clay platelets.