Emma Smart of Daresby Place, Sheffield and Janet Wilson of Fell Road, Ford Estate, Sunderland, claimed repossession action taken against them amounted to a breach of their fundamental rights.
But three appeal court judges dismissed their appeals on Friday.
The women's landlords - Sheffield City Council and Central Sunderland Housing Company Ltd - have already obtained possession orders against them following complaints from neighbours.
But Lord justice Laws, sitting with Lord justice Thorpe and Lord justice Kay, granted them a 'stay of execution' for 14 days so that they can apply to England's highest court - the house of lords - for another appeal hearing.
The judge said complaints of nuisance had been made by neighbours against both women.
Complaints were first made against Miss Smart in January 2000 and, when she celebrated her birthday in July the same year, she 'got drunk' and neighbours asked her to turn her music down.
She was given a warning by the city council but her neighbours complained of another incident in the early hours of the morning of 5 August 2000. She denied responsibility for that disturbance but she was served with notice to quit on 30 August 2000.
In Ms Wilson's case, the judge said complaints appeared to date back to October 1999. 'Thereafter there were other complaints to the effect that youths were congregating about the premises in a way which upset other residents.'
Her landlord's 'Safer Estates Task Force' issued a warning in July 2000 and, when the complaints continued, she was served with notice to quit on 9 August that year.
Both women were taken to court by their landlords and possession orders were issued.
Their counsel, Mr Jan Luba, argued the nature of their non-secure tenancies gave them inadequate protection from eviction and amounted to a breach of their right to 'peaceful enjoyment' of their homes.
Lord justice Laws accepted that judges had to consider the effect of the Human Rights Act before issuing possession orders.
But he told the court: 'They (the women) took the tenancies on terms including the landlord's right to recover possession on service of a good notice to quit.
'Accordingly, when such a right is activated, the tenant is deprived of nothing which he was entitled to keep.'
Despite possession orders having been made against them, both women have remained in their homes pending the outcome of today's appeal.
They now have 14 days in which to petition the house of lords for another appeal hearing. If they are granted leave to appeal - it is only granted in a small minority of cases - the possession orders will be 'stayed' pending the law lords' ruling.
STRAND NEWS SERVICE