* MSCI's index of EM stocks flat

* Dollar weakness helps gain in some EMFX

* Kenyan shilling flat amid presidential elections

Aug 9 (Reuters) - A gauge of emerging market stocks stayed close to a five-week high on Tuesday, while currencies made small moves as investors awaited U.S. inflation data due this week to make bets on the Federal Reserve's next rate move.

Most Asian bourses rose, although gains were capped by declines in Hong Kong stocks . Elsewhere, Hungarian stocks dropped 1.0%, while South Africa's main index surged by the same amount.

MSCI's index of emerging market stocks was flat, having hit a five-week high earlier in the session.

Even amid growth worries, bullishness among analysts in emerging markets has overtaken that in the United States, Citigroup strategists noted, citing their own analysis, with optimism across most sectors apart from the notable exception of financials.

Among emerging market currencies, a weaker dollar lent support to some, although caution ahead of the U.S. consumer prices numbers kept investors from making big bets.

U.S. headline inflation is seen having declined in July, but with labour demand still high, investors have started to price in the likelihood of another 75 basis points rate hike in September.

"If the month-on-month print comes in a little bit lower, markets will then breathe a little bit easier vis-à-vis the Fed," said Peter Kinsella, global head of FX strategy at UBP.

"We're pretty much at or close to peak inflation in the States and that basically means that the dollar should, on balance, weaken very modestly towards year-end," Kinsella said.

"But given the poor growth outlook (globally), it's going to be hard for EM currencies to outperform."

STRONGER CASE

Asian currencies were mixed. South Africa's rand inched up 0.4%, while Mexico's peso climbed 0.2%.

Hungary's forint was steady, but hit session highs against the euro after inflation came in higher than expected, making a stronger case for the central bank to keep tightening interest rates.

Currently at 10.75%, analysts expect the Hungarian base rate to rise to 12% by the end of 2022.

In Ukraine, bondholders have until 5 p.m. New York time (2100 GMT) on Tuesday to decide whether to back a government proposal to defer payments on the war-torn country's international bonds for 24 months to swerve a messy $20 billion default.

Kenya's shilling was flat against the dollar as voting in the presidential election began. Veteran opposition leader Raila Odinga faces off against Deputy President William Ruto.

Markets are scrutinising fiscal accounts, the balance of payments and central bank reserves. Having a current account deficit as well as a fiscal deficit, Kenya's financial position has been a longstanding source of vulnerability.

For GRAPHIC on emerging market FX performance in 2022, see http://tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance in 2022, see https://tmsnrt.rs/2OusNdX

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For CENTRAL EUROPE market report, see

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For RUSSIAN market report, see (Reporting by Susan Mathew in Bengaluru; Editing by David Holmes)