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We define and study the notion of numerical equivalence on algebraiccobordism cycles. We prove that algebraic cobordism modulo numericalequivalence is a finitely generated module over the Lazard ring, and itreproduces the Chow group modulo numerical equivalence. We show this theorydefines an oriented Borel-Moore homology theory on schemes and orientedcohomology theory on smooth varieties.  We compare it with homological equivalence and smash-equivalence forcobordism cycles. For the former, we show that homological equivalence onalgebraic cobordism is strictly finer than numerical equivalence, answeringnegatively the integral cobordism analogue of the standard conjecture $(D)$.For the latter, using Kimura finiteness on cobordism motives, we partiallyresolve the cobordism analogue of a conjecture by Voevodsky on rationalsmash-equivalence and numerical equivalence.

On numerical equivalence for algebraic cobordism