A Lewis acid catalyst composition comprising a specific mixed medium and a Lewis acid catalyst, wherein the Lewis acid catalyst is at least one compound selected from the group consisting of compounds respectively represented by the following formulae (1) and (2):
[(R
f
1
SO
2
)(R
f
2
SO
2
)N]
n
M (1), and
[(R
f
1
SO
2
)(R
f
2
SO
2
)(R
f
3
SO
2
)C]
n
M (2).
A method for continuously performing a reaction which proceeds in the presence of the above-mentioned Lewis acid catalyst by using a specific mixed medium and the above-mentioned Lewis acid catalyst. A novel Lewis acid catalyst.