* Striking miners cheer wage offer
* End in sight to five-month platinum strike
* Lonmin, Implats shares climb, platinum drops
* Strike cost firms $2 billion in lost revenue (Adds Implats spokesman, updates shares)
By Zandi Shabalala
RUSTENBURG, South Africa, June 12 (Reuters) - Workers and shop-stewards from South Africa's AMCU mining union begged leader Joseph Mathunjwa to sign a wage deal with three major platinum firms on Thursday at a mass rally crowning five months of crippling protest.
As the longest strike in the 130-year history of South Africa's mines showed its first signs of breaking, thousands of stick-wielding miners cheered as a senior union official took the microphone to declare: "Sign, Mathunjwa, sign."
Another leader won a similar response when he bellowed: "This union has worked. We want this money. We come from hardships. AMCU has worked. We can't take kids to school. Sign, Mathunjwa."
Mathunjwa, a devout Christian and powerful orator who has become one of the fiercest critics of the inequalities that still bedevil South Africa two decades after the end of apartheid, did not declare an official end to the strike but the reaction from the miners suggests it is near.
Moments before the rally started, the three platinum firms - Anglo American Platinum, Impala Platinum and Lonmin - said they had reached "in principle undertakings" with the leaders of the strike.
"The principles that underpin the proposals seek to achieve a sustainable future for the three platinum companies for the benefit of all stakeholders and to afford employees the best possible increase under the current financial circumstances," Lonmin said.
They did not disclose details of the offer in statements to the stock exchanges in Johannesburg and London.
At first it looked as though the deal might fall through, with miners at the start of the meeting greeting the offer of a 1,000 rand ($93) per month increase with boos and jeers, shouting "Are they mad?"
The offer amounts to a pay hike of nearly 20 percent, but is only a fraction of the roughly 150 percent they were demanding when they first downed tools in January.
"MASSIVE STEP FORWARD"
However, the workers changed their tune during the meeting, to the relief of the platinum firms, who said a formal deal should be signed in the next few days.
"Massive step forward in terms of the ground that was covered today by workers moderating their demands and the parties being close enough to hopefully sign a deal very, very soon," Implats spokesman Johan Theron told SAfm radio.
Shares in Lonmin, the smallest of the big three platinum firms and the one under most pressure, jumped 9 percent.
Impala stock climbed 1.5 percent but gave up those gains to close flat on the day. Anglo American Platinum ended 1.7 percent lower.
The rand, which has been hurt by the loss of foreign currency mine revenue, rallied slightly and the spot price of platinum, used in jewellery and catalytic converters in vehicles, fell more than 2 percent.
South Africa is home to 80 percent of the world's known platinum reserves and the strike has halted production at mines that usually account for 40 percent of global output of the precious metal.
The strike by the 70,000 AMCU members began in January and dragged Africa's most advanced economy into contraction in the first quarter as mining output fell at the steepest rate in half a century, and pulled manufacturing down with it.
It also threatened to destabilise labour relations across South Africa as other groups, in particular the NUMSA metalworkers' union, sharpened their rhetoric and pushed for strikes in pursuit of wage increases way above inflation.
According to a website run by the three companies, the strike has so far cost them 22 billion rand ($2.05 billion) in revenue, while workers have missed out on nearly 10 billion rand in wages.
AMCU burst onto the scene in 2012 when it emerged as the biggest union on the platinum belt after a bloody turf war with the established National Union of Mineworkers.
It hit international headlines in August of that year when 34 of its members, on a wildcat strike at Lonmin's Marikana mine, were gunned down by police in the most deadly confrontation since the end of apartheid in 1994. ($1 = 10.7128 South African Rand) (Reporting by Zandi Shabalala and Olivia Kumwenda-Mtambo; Writing by Ed Cropley; Editing by Stella Mapenzauswa and Ruth Pitchford)