A mood of caution may hang over Asian stocks on Tuesday, following a fairly directionless U.S. session the day before and as investors brace for an interest rate decision in Australia and remarks from Bank of Japan Governor Kazuo Ueda.

That said, the slender gains eked out on Wall Street kept the S&P 500 within 0.3% of last week's record high, and pushed the Dow to a new peak of 42,190 points. The feel-good factor from last week's Fed move has not faded just yet.

Indeed, the bullish case for risky assets may have gotten a boost on Monday from Chicago Fed president Austan Goolsbee, who said the Fed's policy rate is still "hundreds" of basis points above neutral and that there are "a lot of cuts" to come over the next year.

This follows surprisingly dovish comments on Friday from Fed Governor Christopher Waller, who said inflation is softening much faster than he previously thought and August PCE inflation could be very low.

But there's often a fine line between deep rate cuts encouraging investors to load up on risk, and concerns over why policy is being loosened so much so quickly. This is why all economic activity and labor market data between now and the Fed's next meeting will be scrutinized so closely.

The Reserve Bank of Australia is the next major central bank to deliver its latest policy decision and guidance. With inflation running above the central bank's 2%-3% target range and the job market looking strong, there is virtually no chance of a rate cut yet.

All 43 economists polled by Reuters expect the RBA to keep its cash rate on hold at 4.35% on Tuesday, and 40 of them say there will be no move on rates this year.

Aussie swaps markets are attaching a roughly two-in-three chance of a 25 basis point rate cut by the end of this year, and imply a full 100 bps of easing next year - significantly less than all G10 central banks except the Bank of Japan and Swiss National Bank.

The BOJ is the only major central bank raising rates, and investors will be looking to a speech from Governor Kazuo Ueda on Tuesday for clues on the pace and extent of tightening. The BOJ left rates unchanged on Friday and signaled it is in no rush to raise them again.

The People's Bank of China, meanwhile, injected 14-day liquidity into the financial system on Monday for the first time in months, and at a lower rate than before. But investors will need a lot of convincing that Beijing's stimulus efforts will be enough to fight off deflation and revive growth.

Here are key developments that could provide more direction to Asian markets on Tuesday: