Tube and union bosses met at the negotiating table on Tuesday to try to resolve a long-running pay dispute.
Tube strikes led to a crush on the buses
Two strikes crippled the London Underground (LU) network in October 2002, before mayor Ken Livingstone agreed to go to mediation.
LU managers met union leaders at the conciliation service ACAS in August, but failed to reach an agreement after two days of talks.
Now unions are warning another dispute may delay any long-term deal.
The Rail, Maritime and Transport union (RMT) has accused two private companies in charge of the Tube's tracks and signalling of reneging on a pay deal hammered out in 2003.
It wants staff employed by Metronet and Tube Lines to have a pay increase of 0.75% - awarded in 2003 - back-dated 16 months to bring them in line with other LU workers.
Bob Crow, the general secretary of the RMT, said legal advice obtained by the union made it clear the companies should honour the deal brokered by Mr Livingstone.
The companies have agreed to back-date the pay offer, but only to April 2003 when they took over under the public/private partnership scheme for LU.
LU says the responsibility now lies with the private firms.
The train drivers' union Aslef has warned the dispute may stall plans for a three or four-year pay deal on the Tube.