  We have searched for the leptonic and radiative leptonic B decays, B^+ ->
mu^+ nu, B^+ -> e^+ nu gamma and B^+ -> mu^+ nu gamma. Using a 140 fb^{-1} data
sample collected with the Belle detector at the KEKB asymmetric e^+ e^-
collider, we find no evidence for signals in any mode and set the following
preliminary upper limits at 90% confidence level:
  BR(B^+ -> mu^+ nu) < 2.0 * 10^-6,
  BR(B^+ -> e^+ nu gamma) < 2.2 * 10^-5, and BR(B^+ -> mu^+ nu gamma) < 2.3 *
10^-5.
