The paper discusses the analytical investigation of the occurrence of coherent optical transient processes such as dynamic Stark effect and free induction decay in direct-gap semiconductor quantum wires with thickness and width smaller than the bulk Wannier-Mott exciton Bohr radius. The role of a moderately strong magnetic field has been critically evaluated in the occurrence of the transient processes. The analysis is based upon the time dependent perturbation treatment of the coherent radiation-semiconductor interaction model under near band gap resonant excitation regime. The excitation intensity is kept below the Mott transition regime. Numerical estimates made for a GaAs/AlGaAs quantum wire irradiated by femtosecond pulse Ti:Sapphire laser establishes that the Stark shift, Stark broadening as well as free induction decay are all considerably influenced by the magnetic field. Moreover, the wire width also affects Stark splittings.