  We describe a large class of exact string backgrounds with a null Killing
vector arising, via a limiting \`a la Penrose procedure, from string
backgrounds corresponding to coset conformal field theories for compact groups
G_N/H_N times a free time-like boson U(1)_{-N}. In this way a class of novel
logarithmic conformal field theories (LCFT) emerges, that includes the one
constructed recently as an N\to \infty limit of the SU(2)_N/U(1) X U(1)_{-N}
theory. We explicitly give the exact operator algebra for the basic chiral
fields as well as their representation in terms of free bosons, even though
these are not known in general at finite N. We also compute four-point
functions of various operators in the theory. For the cases of the four- and
five-dimensional models, corresponding to a limit of the theory SO(D+1)_N/SO(D)
X U(1)_{-N} for D=3 and 4, we also present the explicit expressions for the
background fields.
