Adopting an approach similar to that of Zukowski [Phys. Rev. A 62, 032101 (
2000)], we investigate connections between teleportation and nonlocality. W
e derive a Bell-type inequality pertaining to the teleportation scenario an
d show that it is violated in the case of teleportation using a perfect sin
glet. We also investigate teleportation using "Werner states" of the form a
lphaP(s) + (1 - alpha )l/4, where P-s is the projector corresponding to a s
inglet state and I is the identity. We find that our inequality is violated
, implying nonlocality, if alpha> 1/root2. In addition, we extend Werner's
local hidden variable model to simulation of teleportation with the alpha =
1/2 Werner state. Thus teleportation using this state does not involve nonl
ocality even though the fidelity achieved is 3/4, which is greater than the
"classical limit" of 2/3. Finally, we comment on a result of Gisin's and o
ffer some philosophical remarks on teleportation and nonlocality generally.