* Xi visits Beijing university, first public appearance in two weeks
* Pictures show him looking well, laughing
* Rumours had flown about his health, Xi had missed meeting with Clinton
* Communist Party gearing up for tricky leadership succession
By Chris Buckley and Ben Blanchard
BEIJING, Sept 15 (Reuters) - Chinese leader-in-waiting Xi Jinping appeared in public on Saturday for the first time in about two weeks, visiting a Beijing university in what appeared to be an effort to dispel rumours of serious illness and a troubled succession.
In a brief English-language report that broke the official silence on his whereabouts, the Xinhua news agency said Vice President Xi had arrived at China Agricultural University in the morning for activities to mark National Science Popularisation Day.
Pictures on state television's main evening news showed a healthy-looking, relaxed Xi inspecting ears of corn, chatting with students and laughing with children. Reuters had reported that Xi was likely to make an appearance on Saturday.
Sources said Xi hurt his back while swimming earlier this month and that he had been obeying doctors' orders to get bed rest and undergo physiotherapy.
A Reuters reporter at the university saw a man with sleek black hair wearing a white shirt -- who from a distance looked like Xi -- getting loud applause as he stepped out of the building housing an exhibition and raised his arms up and down twice in a gesture of vigour.
A later, full description of Xi's visit by Xinhua said he inspected exhibitions on growing drought-resistant corn and a talk on how to fight food adulteration, a perennial problem in the world's second-largest economy.
"Food is the people's first necessity, and food safety is an important issue for people's livelihood," the report quoted him as saying.
None of the reports made mention of Xi's recent absence.
News of his appearance spread rapidly on China's popular Twitter-like microblogging site Sina Weibo, with users referring to Xi as the "crown prince" to avoid the usual censorship associated with the names of top leaders.
"He looks well," wrote one user.
"In the future he should take better care when he goes swimming," added another.
Xi had been out of the public eye for almost two weeks and had skipped meetings with foreign leaders and dignitaries, including U.S. Secretary of State Hillary Clinton.
Chinese government officials repeatedly refused to say what had happened to him, fuelling speculation that has included Xi supposedly suffering a heart attack, a stroke, emergency cancer surgery and even an attempted assassination.
The ruling Communist Party's refusal to comment on his disappearance from public view and absence from scheduled events was in keeping with its traditional silence on the question of the health of top leaders - long considered a state secret - but it had worried or mystified most China watchers.
Beijing has yet to announce formally a date for the party's five-yearly congress, at which Xi is tipped to replace Hu Jintao as party chief, although it is still expected to be held in mid- or late October at the earliest.
In March next year, he is formally to take over the reins of the world's second-largest economy.
The uncertainty surrounding Xi's absence has had no impact so far on Chinese or foreign markets, which have been absorbed by Europe's debt crisis and China's own economic slowdown. But investors have been keeping a close eye on the mystery surrounding Xi, after months of political drama in China.
Senior leader Bo Xilai was suspended from the party's 25-member Politburo in April and his wife convicted of the murder of a British businessman. Blind human rights activist Chen Guangcheng escaped from house arrest in April and took refuge in the U.S. embassy before leaving for New York.
In another scandal this month, a senior ally of President Hu was demoted after sources said the ally's son was killed in a crash involving a luxury sports car.