Uncertainty about the health of the economy means the Fed is unlikely to raise rates on Wednesday. Instead, expect it to say that it will increase rates when unemployment falls and inflation expectations rise - something economists believe we could see by September.
In the UK, the main development could be a rise in inflation. CPI inflation on Tuesday could turn positive. This will be partly because there were big falls in food and petrol prices last May which will drop out of the annual data. However, higher petrol prices and air fares this May could push inflation up.
We'll also see signs of inflation elsewhere. Producer price data the same day could show a fourth successive small monthly rise in both input and output prices - although the annual rates of inflation are still negative and rises are capped by the strength of sterling. And on Wednesday we might see another pick-up in annual wage growth, to around 2 per cent on a three-month average basis. In itself, this is not inflationary. If, however, it is accompanied by a continued stagnation in productivity, the Bank of England will be concerned that higher unit wage costs might add to inflation.
How concerned they are will be evident in Wednesday's minutes of their recent meeting. It's possible that one or two members are considering raising rates, although their desire will have been tempered by unexpectedly weak growth in the first quarter.
That weakness, however, might be only temporary. Thursday's figures could show that retail sales fell only slightly in May after a big rise in April, implying annual growth of over 4 per cent in volume terms. This would suggest that strong consumer spending is driving growth upwards.
One other thing investors should watch for is net foreign buying of US equities, contained in the US Treasury's data on capital flows on Monday. Last month, foreigners were net sellers. Historically, such selling has predicted high returns on global equities in the following 12 months, as it is a sign of unusually depressed sentiment.
