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Higher dimensional cosmological implications ofa decay law for the cosmological constant term are analyzed. Three independent cosmological models are explored mainly: 1) - In the first model, the effective cosmological constant was chosen to decay with times like Λeffective = Ca-2 + D(b/ai)2 where aiis an arbitrary scale factor characterizing the isotropic epoch which proceeds the graceful exit period. Further, the extra-dimensional scale factor decays classically like b(t) ≈ ax (t),xisareal negative number. 2) - In the second model, we adopt in addition to Λeffective = Ca-2 + D(b/ai)2 the phenomenological law b(t) = a(t) exp(-Qt) as we expect that at the origin of time, there is no distinction between the visible and extra dimensions; Qis a real number. 3) -In the third model, we study a Λ-decaying extra-dimensional cosmology with a static traversable wormhole in which the four-dimensional Friedmann-Robertson-Walker spacetime is subject to the conventional perfect fluid while the extra-dimensional part is endowed by an exotic fluid violating strong energy condition and where the cosmological constant in (3+n+1) is assumed to decays like Λ(a) = 3Ca-2. The three models are discussed and explored in some details where many interesting points are revealed.

Implications of a decay law for the cosmological constant in higher dimensional cosmology and cosmological wormholes