Let
R
R
and
S
S
be positive integers with
R
>
S
R>S
. We shall call the simultaneous Diophantine equations
x
2
−
R
y
2
a
m
p
;
=
1
,
z
2
−
S
y
2
a
m
p
;
=
1
\begin{align*} x^2-Ry^2&=1,\ z^2-Sy^2&=1 \end{align*}
simultaneous Pell equations in
R
R
and
S
S
. Each such pair has the trivial solution
(
1
,
0
,
1
)
(1,0,1)
but some pairs have nontrivial solutions too. For example, if
R
=
11
R=11
and
S
=
56
S=56
, then
(
199
,
60
,
449
)
(199, 60, 449)
is a solution. Using theorems due to Baker, Davenport, and Waldschmidt, it is possible to show that the number of solutions is always finite, and it is possible to give a complete list of them. In this paper we report on the solutions when
R
>
S
≤
200
R>S\le 200
.