Coasting cosmologies with time dependent cosmological constant

The effect of a time dependent cosmological constant is considered in a fam ily of scalar-tensor theories. Friedmann-Robertson-Walker cosmological mode ls for vacuum and perfect fluid matter are found. They have a linear expans ion factor, the so-called coasting cosmology, the gravitational "constant" decreases inversely with time; that is these models satisfy the Dirac Hypot heses. The cosmological "constant" decreases inversely with the square of t ime, therefore we can have a very small value for it at present time.