The illness and death of Emperor Hirohito meant months of problems for the Japanese press. Some problems were uniquely Japanese, others not so different from those in our own system.

The chief lesson we can get from the way the story was handled in Japan is this: Governments invite excessive speculation and erroneous reports when secrecy is obsessive, doubly so when it is unnecessary.The emperor's condition was the big story in Japan from Sept. 19, when the ailing monarch took a turn for the worse, until his death Jan. 6. But precious little information came out of the court in the early weeks. The cabinet and prime minister's office complained that the imperial household and the court physicians were volunteering too little even to keep key government officials in the know.

The press had even less information. For it, the death watch became grueling and expensive. The public broadcasting service, NHK, reported spending more than $100,000 a day in staff costs on the story. To garner and piece together snippets of information, the papers and broadcasters stationed at least 2,300 reporters, an enormous number even by Japanese standards, 24 hours a day at the Imperial Palace and other strategic spots around Tokyo.

Inevitably, some reports went awry. On Sept., 26, an editorial in the Mainichi Daily News, the English-language edition of another of the Tokyo giants, expressed sorrow over the emperor's "death." That lapse hasn't been explained, only that the paper, grievously embarrassed, recalled its entire press run.

Fatigue was a factor. By Nov. 10 it had "reached a limit" in the press, according to the newsletter of the Japanese Newspaper Association.

- REPORTS SURFACED on Oct. 24 that the emperor was suffering from cancer. The first was carried in Asahi Shinbun (Rising Sun newspaper), one of the Tokyo Big 3 newspapers and the second largest (13 million copies a day).

Asahi's story was bold because Japan has had a long ongoing debate on whether any cancer patient should ever be informed of the nature of his illness. Both Asahi and Kyodo news service, which followed with a similar report, were criticized severely when the emperor's condition stabilized briefly.

The irony is that the palace became more cooperative with the press after the Asahi and Kyodo reports broke the taboo. It began providing more frequent and more detailed statements about Hirohito's condition.

- THE FATIGUE of the Japanese populace under the unremitting demand for "self restraint" in public activities in deference to the emperor also led to some complaints against the papers. In effect, the press fed the public mood of grieving by continually featuring it. TV refrained from broadcasting frivolous programs. Businesses toned down advertising. Merrymaking, recreation and festivities were reined in, even during the holiday season, despite the crown prince's statement that "excessive voluntary restraint runs counter to the will of the emperor."

Ultimately the Japanese population was as worn out as the press. As National Public Radio reported last week, deep condolences from the American government actually went beyond what most Japanese expressed, because they felt they already had grieved enough.

- THE RELUCTANCE of authorities to level with the population on the ailments of monarchs may seem quaint to us. But in truth it is not too different from how reports of illnesses of our presidents have been handled in the not-distant past.

Until after John F. Kennedy, the staffs of our ill presidents have kept the nature of their ailments secret or have deliberately lied.

These presidents include Kennedy, whose bad back was legendary but whose Addison's disease wasn't discussed. Woodrow Wilson not only suffered a stroke but was incapacitated by it, unable to perform the duties of office. The electorate did not know that Franklin D. Roosevelt suffered hypertension and heart failure when he ran for a fourth term in 1944.

The American media have become more penetrating and candid about all aspects of public officials' lives, including their health, with one major exception. Ronald Regan was more perilously hurt, indeed lost half his blood, in the 1981 assassination attempt than his aides, who wanted to reassure the public and avoid passing temporary power to the vice president, would let on.

- REPORTING OF the Japanese imperial family is also bound to change because of the experiences of reporting the emperor's illness and because the new emperor is more modern and accessible.

The change really began a year earlier, in September 1987, when Asahi's imperial family reporting team broke the initial story of the emperor's illness and his abdominal operation. Asahi's imperial household reporting team won the Japan Newspaper Association's 1988 award, akin to our Pulitzers, for its enterprise.

By somehow penetrating what the Japanese call the palace's "chrysanthemum curtain," the paper, as the citation put it, "changed the conventional method of reporting on the imperial family and caused a re-examination of the way public information of the imperial family is carried out."

Now the Japanese are asking whether other taboos surrounding the royal family, including the question of the emperor's responsibility in World War II, will be open to public examination, as they should be in an open society.