Rational approximants are defined from double power series in variables x and y, and it is shown that these approximants have the following properties: (i) they possess symmetry between x and y; (ii) they are in general unique; (iii) if
x
=
0
x = 0
or
y
=
0
y = 0
, they reduce to diagonal Padé approximants; (iv) their definition is invariant under the group of transformations
x
=
A
u
/
(
1
−
B
u
)
,
y
=
A
v
/
(
1
−
C
v
)
x = Au/(1 - Bu),y = Av/(1 - Cv)
with
A
≠
0
A \ne 0
; (v) an approximant formed from the reciprocal series is the reciprocal of the corresponding original approximant. Possible variations, extensions and generalisations of these results are discussed.