In last weekend's first round Mr Kuchma, who wants faster progress to a market economy and close ties with Western Europe, won 36.5 per cent of the vote; his main challenger, Petro Symonenko, got 22 per cent.
Though Mr Kuchma remains a narrow favourite, signs were growing that Mr Symonenko could forge a coalition, with candidates defeated in the first round, capable of bringing him down. Mr Kuchma's response was to sack the governors of Vinnitska, Kirovograd and Poltava, where the left was victorious on 31 October.
Ukraine and other states which replaced the southern republics of the former Soviet Union are watching with growing concern Moscow's onslaught on Chechnya, seen by many as sign of a resurgent Russian nationalism.
In his way too Mr Kuchma is vulnerable to such trends, having failed to prevent a worsening of the economy, saddled by debts (not least to Russia) and trapped in an inefficient and corrupt "market-Leninism".
Nearer Chechnya, apprehensions are greater still. In Georgia, parties backing President Eduard Shevardnadze won a comfortable victory in weekend parliamentary polls over a pro-Russian alliance, suggesting that Mr Shevardnadze, who favours close ties with the West and membership of Nato, will win spring's presidential vote.
But Georgia's border with Chechnya, the insurgent republic's only link with the outside world, means it could get sucked into the conflict.
These fears grew yesterday as Vladimir Putin, the Russian Prime Minister, demanded that Georgian citizens obtain visas before entering Russia. The move came after Russian commanders complained that the Georgian government had refused to take part in joint patrols along the mountainous Georgian- Chechen frontier.