1.200 people stand in a circle, some of whom are honest people, and some are liars. Liars always tell lies, while honest people tell the truth depending on the situation. If both of his neighbors are honest people, he will definitely tell the truth; if at least one of his neighbors is a liar, he may sometimes tell the truth and sometimes lie. It is known that among these 200 people, 100 people say they are liars, and 100 people say they are honest. How many honest people can there be at most in these 200 people?
1. There can be at most 150 honest people.

Since liars do not say they are liars, the 100 people who say they are liars are all honest people, and what they say is false. This indicates that they are all adjacent to liars.
Since each liar is adjacent to at most two honest people, there must be at least 50 liars. This indicates that the number of honest people will not exceed 150.
Next, let's provide an example.
150 honest people are divided into 50 groups, with 3 honest people standing together in each group, and one liar between each group.
The honest person in the middle of each group tells the truth, saying they are honest, while the honest people at the ends of each group lie, saying they are liars, and the 50 liars all say they are honest.