What concern did Romans have about Julius Caesar?

They were afraid that he will introduce some type of dictatorship in the country and take the full authority in his hands. Rome was a Republic and people believed that other forms of government are unacceptable.

Explanation:

Julius Caesar was a great warrior, general, even a writer. But, when he emerged as a leading figure in Rome, some people, especially in the Senate were afraid that he will destroy the order in the country. Romans had in their memory a period of Kings that lasted for almost 250 years, and have vowed not to allow anyone to reign as the kings did. That is why some of them plotted to kill Caesar.