TOKYO, July 29 (IFR) - Japanese government bonds were mostly steady after a quiet morning session characterised by low trading activity as investors looked ahead to several key events and data this week.

Later in the session, the U.S. Federal Reserve will begin a two-day meeting, which many believe is likely to culminate in the same dovish message from Chair Janet Yellen.

The Commerce Department is expected to report on Wednesday that the economy grew at a 3.2 percent annual pace in the second quarter, after it shrank 2.9 percent in the previous quarter. Then on Friday, the Labor Department's nonfarm payrolls are expected to show a rise of 231,000 in July after they increased 288,000 in June, and the jobless rate is expected to hold steady at 6.1 percent.

JGB futures traded in an extremely narrow 145.95-146.00 range in the morning session, which was established within 30 minutes after the open. They finished at midday up 0.02 point at 145.99.

There was no major buying this morning and the theme of "don't-sell-a-quiet-market" supported futures, according to a trader at a foreign investment bank's futures desk.

Cash bonds were somewhat top-heavy in 10- and 20-year zones, where yields added half a basis point to 0.525 percent and 1.380 percent respectively. The 30-year yield remained unchanged at 1.645 percent .

A speech by Bank of Japan policy board member Koji Ishida provided no clues on possible revision of the central bank's outlook on the economy and prices.

Ishida said the environment surrounding exports will likely gradually improve as global growth picks up, but warned of uncertainties such as structural factors that may weigh on overseas shipments in the long term.

(Reporting by Takahiro Okamoto; Editing by Shri Navaratnam)