We determine all
(
1
,
1
)
(1,1)
-knots which admit an essential meridional surface, namely, we give a construction which produces
(
1
,
1
)
(1,1)
-knots having essential meridional surfaces, and show that if a
(
1
,
1
)
(1,1)
-knot admits an essential meridional surface, then it comes from the given construction.