An ICM poll for Scotland on Sunday puts the Yes vote on 39% (no change on a month before), while No was on 42% (down four points).
Survation's research for the Sunday Post found Yes on 38% (up one point on a previous poll 10 days earlier) and No on 46% (one point down).
Professor John Curtice, writing on his WhatScotlandthinks blog, says: "The headline results of the two polls will doubtless be regarded as encouraging for the Yes side.
"But underneath the bonnet there are also signs that the No vote may have become a little more resilient...according to ICM, as many as 89% of No voters have definitely made up their mind, compared with only 78% of Yes supporters. The former figure is up seven points on the equivalent figure for last month, whereas the latter is only up one.
"When voters are asked to compare the trustworthiness of the two sides directly... 29% say they trust the Yes side more, only 21% say the same of the No side...as many as 39% say that neither side is trustworthy, a feeling that is particularly widespread amongst undecided voters.
"Both of today's polls point to a race that continues to look much closer than it did just a few short months ago."
Yes Scotland chief executive Blair Jenkins said: "The extreme negativity of the 'no' campaign is proving a major turn-off for voters, and month by month they are paying the price."
The polls were published as it emerged Labour is planning to step up campaigning in Scotland.
Ed Miliband's shadow cabinet will hold a meeting in Glasgow on Friday, while MPs will campaign across the country over the week.
Meanwhile, former prime minister Gordon Brown will focus on the security of pensions as he makes the case for the union during a speech for Better Together in Glasgow.
Yes Scotland is stepping up activity with the launch of a new billboard poster campaign explaining why the country "must" be independent.
Blair Mcdougall, director of Better Together, said his group will also launch an advertising campaign this week.
"Whilst it is welcome that there is a majority in favour of keeping the UK together, these polls are a reminder that there can be no complacency from those who believe that the brightest future for Scotland is to remain in the UK," he said.
"With the launch of our advertising campaign tomorrow and a big grassroots campaign push we will be fighting hard for every single vote between now and polling day. Everybody who wants to keep Scotland in the UK needs to play their part."