A look at the day ahead in European and global markets from Vidya Ranganathan

U.S. and UK markets return from their long weekend on Tuesday with a touch of ambivalence, happy that the weekend resulted in a U.S. debt ceiling agreement and yet anxious about how the deal will fare in congress.

More detail and clarity are expected around the tentative agreement in Washington to suspend the $31.4 trillion federal debt ceiling until January 2025 in exchange for caps on spending and cuts in government programmes. Even before celebrations could begin, a handful of hard-right Republican lawmakers have said they will oppose it.

That means the bipartisan 99-page bill, still subject to approval in both houses of congress, could face a rocky path before the U.S. runs out of money next week.

Meanwhile, Spanish Prime Minister Pedro Sanchez surprised everyone, even people within his own government, by taking "personal responsibility" for Sunday's crippling defeat in a regional election and calling for a snap election next week.

It seemed to be an attempt to wrong-foot his conservative opponents and give his flagging Socialist party the best chance of retaining power before its support weakens further.

In the first trades in U.S. debt markets since the debt ceiling deal, longer-term Treasuries rallied in Asia, driving benchmark 10-year yields down 6 basis points to 3.76%.

But bid-offer spreads were wide in Asia, as investors balanced their nerves over the deal's passage, the prospect of Treasury potentially issuing more than $1 trillion in bills in the coming months to replenish its coffers, and suspicion that the Fed will have to raise rates further.

Asian stocks are up, and futures indicate mild gains for stocks in Europe and the United States, too. The dollar is staying firm around its strongest level in more than two months against a basket of major currencies.

Besides the debt deal, there is little else on investors' minds. Spain kicks off a week of European inflation readings, all of which should show some moderation in prices and yet not enough to change expectations for more policy tightening.

Key developments that could influence markets on Tuesday:

Speakers: Richmond Fed President Barkin (FOMC non-voter), Representatives from SWFs and the SWF industry gather in London for the Global Wealth Conference.

Data: U.S. Conference Board Consumer Confidence Index, EU Consumer Confidence, U.S. House Price Indices, Dallas Fed Manufacturing Activity (May), Sweden Q1 GDP, Switzerland Q1 GDP.

Earnings : Manchester United, Hewlett-Packard

(Reporting by Vidya Ranganathan; Editing by Edmund Klamann)