James C. Hughes, brought in a year ago to run C3 Inc., resigned yesterday from the Herndon-based computer company amid rumors that the company is experiencing severe financial difficulties.

Hughes, formerly a top executive at BDM International Inc., was hired for $185,000 by Knoll Capital Management L.P., the New York investment firm that acquired C3 for $133 million after a bitter, nine-month takeover battle that ended in May 1989.

Samuel Strickland, C3 chief financial officer, declined to say why Hughes resigned as president and chief executive.

The company issued a statement yesterday announcing the Hughes resignation. The statement included a statement by Fred Knoll, head of the investment company and chairman of C3, thanking Hughes for his "dedication and commitment to C3."

The statement did not say why Hughes resigned or what he planned to do. Strickland said no replacement had been named. Hughes and Knoll could not be reached for comment.

Sources said that John Riceman, C3 executive vice president, also planned to resign, but Strickland said: "We have no announcement to that effect."

The resignation of Hughes, and potentially of Riceman, had been rumored in the government contracting industry recently. Also, several sources in the local financial industry said they believe that C3 is having financial problems.

C3's Strickland would say only, "We're not swimming in cash, but we don't have any problems today."

The payment on C3's debt, which is held by UBS Securities Inc., a New York investment firm, comes due June 30, Strickland said. He declined to comment on whether the company could meet its first payment. Strickland said the company had not made any announcements on how it planned to handle meeting the payments.

C3's fiscal year ended March 31, but year-end figures have not been released. For the nine months ended Dec. 31, C3 lost $17.7 million, compared with earnings of $833,000 in the first nine months of the previous fiscal year. Revenue totaled $42.4 million, down 21 percent from the nine months ended Dec. 31, 1988.

The bruising takeover battle over C3 left the company about $80 million in debt, giving it about three times as much debt as equity. The company reported that it had $4.6 million in interest expenses in the third quarter.