Tenants in Montgomery County who have let their apartment leases run out but are continuing to rent on a month-to-month basis got an extra measure of security last week.

Because of an act of the General Assembly, passed earlier this year but effective beginning last Friday, landlords must give holdover tenants two months notive when they tell the tenants to leave. The tenants, however, will only have to give the usual one month's notice of their departure.

The new law applies to all residential leases in Montgomery County, except leases of single family dwellings. Del. Donald Robertson, (D-Chevy Chase), chairman of the Montgomery delegation, said legislators enacted the law because they felt one month's notice of an eviction was too short.

Although the law has just gone into effect, landlords are already unhappy about it because of the different standards it sets for landlords and tenants, according to Elise Hall of the Montgomery County office of landlord-tenant affairs.

In order to overcome what they say is a disadvantage, some landlords have been taking about changing leases to require a two-month notice by both parties, Hall said.

In a related matter, Thomas N. Hamilton, director of the Montgomery landlord-tenant office, reminded all of the county's licensed landlords that a county ordinance requires them to give tenants a special statement about the service his office offers whenever tenants are notified of overdue rent or eviction.

The landlord-tenant office, which monitors the 47,000 rental units in Montgomery County, is located at 8728 Colesville Rd., Silver Spring, and may be reached by calling 587-5939.