We investigate the status of models containing exotic fermions or extra Z-like neutral gauge bosons in the light of the recent data on anomalous magnetic moment of muon. We find that it is possible to extract interesting bounds on the parameters characterizing such models. The bounds are particularly strong if the new flavourchanging neutral currents are axial vectorlike.The recent measurement of the anomalous magnetic moment (a µ ) of the muon by the E821 experiment [1] at BNL may very well act as an Occam's razor in constraining physics beyond the Standard Model (SM). The data seem to indicate a 2.6σ deviation from theoretical predictions based on the SM. More precisely, the measured value a µ ≡ (g µ − 2)/2 lies in the range a exp µ = (11 659 202 ± 14 ± 6) × 10 −10 (1) in units of the Bohr magneton (e/2m µ ). Accumulation of fresh data is likely to reduce the errors even further. Comparing this with the SM prediction [2] of a SM µ = (11 659 159.7 ± 6.7) × 10 −10 ,one has a rather tantalizing allowance for contributions from a number of non-standard options [3][4][5][6]. At the same time, it is possible to constrain new theories with potential extra contributions to (g µ − 2). This is especially true, as is evident from equations (1) and (2), for scenarios where the additional contributions to the magnetic moment can be negative. One such set of possibilities consists of models with exotic fermions and/or extra neutral gauge bosons [7]. In this note we shall examine constraints on parameters of these models, such as the couplings and the masses of these extra particles, that can be imposed from the new measurement of the muon anomalous magnetic moment. *