  Two series of W-algebras with two generators are constructed from chiral
vertex operators of a free field representation. If $c = 1 - 24k$, there exists
a W(2,3k) algebra for k in $Z_{+}/2$ and a W(2,8k) algebra for k in $Z_{+}/4$.
All possible lowest-weight representations, their characters and fusion rules
are calculated proving that these theories are rational. It is shown, that
these non-unitary theories complete the classification of all rational theories
with effective central charge $c_{eff} = 1$. The results are generalized to the
case of extended supersymmetric conformal algebras.
