* China, HK shares down on weak trade data
* Country Garden misses bond payments
* Hungary July CPI slows, meets forecast
* Pakistan's Imran Khan challenges conviction
Aug 8 (Reuters) - Most emerging market stocks and currencies fell on Tuesday, on concerns over continued slowdown in second-largest economy China following weak trade data, while Hungary's forint gained as traders stuck to their bets of a gradual policy easing.
China's blue-chips and Hang Seng indexes fell 0.3% and 1.8% respectively, after weak data on July imports and exports reinforced fears of further economic slowdown in third quarter, heightening pressure for fresh stimulus.
Chinese developers also fell 4.8%, after Country Garden's failure to pay two dollar bond coupons due on Aug. 6 confirmed fears of the nation's biggest privately owned developer slipping into repayment troubles.
The MSCI index for EM stocks lost 1.0%, touching a three-week low intraday, with traders keenly awaiting U.S. and China inflation prints.
The MSCI EM currencies gauge fell 0.3%, hitting a near one-month low during the day, with China's yuan slipping 0.3% against the U.S. dollar.
In Central and East Europe, Hungary's headline inflation slowed to an annual 17.6% in July, matching expectations, with Economic Development Minister Marton Nagy noting that the rate will fall to single digits by October.
Hungary's forint, however, gained 0.4% against the euro ahead of the July policy meeting minutes due on Wednesday.
"The July inflation indicator is unlikely to have a significant impact on monetary policy," said Peter Virovacz, senior economist at ING in Budapest.
"Primary, post-data market reactions suggest that investors are dismissive of the possibility of more aggressive rate cuts in response to the disinflation seen... perhaps why we have seen the forint begin to strengthen again."
Romania's leu remained unchanged, largely holding on to Monday's action, after the central bank kept its benchmark rate on hold at 7%.
Meanwhile, Polish central banker Przemyslaw Litwiniuk said cutting rates this autumn would be a mistake amid speculation that policy easing could be just around the corner.
While the Polish zloty slipped 0.2%, Czech crown was flat.
Traders will also keep an eye out for Russian, Czech and Romanian inflation data due this week.
Russia's rouble weakened past 96-per-dollar, heading back towards a more than 16-month low, hampered by strong local demand for foreign currency.
Meanwhile, traders monitored developments around the jailing of Pakistan's former premier Imran Khan, whose lawyer said he challenged his conviction on graft charges in a high court on Tuesday.
The Pakistani rupee and stocks were down 0.9% and 0.8%, respectively.
Pakistan International Airlines, however, jumped 9% on the government's plan to privatise the loss-making national carrier. (Reporting by Ankika Biswas in Bengaluru; Editing by Varun H K)
