The 9"x9" tiles you have are Vinyl Asbestos Tile (VAT). They are no longer available today. Some people have cut-down 12"x12" Vinyl Composition Tiles (VCT) to look more like the original tiles, however unless you have the appropriate tools this can be very labor intensive.
Cutting Down 12"x12" Floor Tiles
Vinyl-asbestos tile is dependable and durable and it does not pose harm unless it is disturbed. It was the tile of choice for decades until it was discontinued for residential application in 1973. Manufacturers had until 1978 to deplete their stock and cease distribution. Asbestos had been used for almost 100 years as a binder in tiles. The asbestos in tile is not considered a health hazard because it is not friable or airborne. When removed however, it can become airborne and appropriate precautions should be taken or a professional abatement should be done.
If you would like additional information regarding asbestos and it's effects, here is a very informative webpage that simply states the different types and conditions where it is typically found:
Asbestos Information Link