AclassoffunctionscalledquasiB,-invexandpseudoB,-invexfunctionsareintroducedbyusingtheconceptofsymmetricgradient.TheexamplesofquasiB,-invexandpseudoB,-invexfunctionsaregiven.ThesufficientoptimalityconditionsandMond-Weirtypedualityresultsareobtainedforanondifferentioblenonlinearsemi-infiniteprogrammingprobleminvolvingquasiB,-invexandpseudoB,-invexfunctions.