Rare decays of beauty particles were studied in several charmless mode
s using the data collected with the DELPHI detector at LEP from 1991 t
o 1994. These decays are mediated by both tree level b-->u and one-loo
p penguin b-->s, d transitions. Evidence for charmless B decays was ob
tained in two body hadronic modes. The branching ratios of B-d,s(0) to
pi(+)pi(-) or K(+)pi(-) and B-u(-) to rho(0) pi(-) or K(0)pi(-) were
found to be (2.8(-1.0)(+1.5) +/- 0.2) x 10(-5) and (1.7(-0.8)(+1.2) /- 0.2) x 10(-4) respectively. The fraction of these decays with a cha
rged kaon in the final state that is not from the spectator s quark, w
as measured to be 0.58 +/- 0.18. Upper limits were set at 90% confiden
ce level on the branching ratios for three and four body charmless had
ronic decays in the range of (1-3) x 10(-4), for inclusive radiative b
-->s gamma decays at 5.4 x 10(-4), for inclusive radiative b-->s gamma
decays at 5.4 x 10(-4), for the exclusive radiative decays B-d(0)-->K
(892)(0) gamma and B-s(0)-->phi(1020)gamma at 2.1 x 10(-4) and 7.0 x
10(-4) respectively, and for dineutrino decays, b--><s nu(nu)over bar>
, in the exclusive channels B-d(0)-->K(892)(0) nu<nu(nu)over bar> and
B-2(0)-->phi(1020)<(nu nu)over bar> at 1.0x10(-3) respectively. The l
imits on dineutrino decays constrain theories with a new U(1) gauge bo
son coupling predominantly to the third family of fermions.