  New deformations of the Poincare group $Fun(P(1+1))$ and its dual enveloping
algebra $U(p(1+1))$ are obtained as a contraction of the $h$-deformed
(Jordanian) quantum group $Fun(SL_h(2))$ and its dual. A nonstandard
quantization of the Heisenberg algebra $U(h(1))$ is also investigated.
