It has been proved in the paper [4] that provided a space of pseudoholomorphic functions is given, one can construct operatorsLsuch that the initial value problem of Cauchy-Kowalewski typeturns out to be solvable by the abstract Cauchy-Kowalewski theorem in any case. Moreover the solution belongs to the associated space defined by the ordinary differential equation of the formwheredenotes theE-derivative of theE-pseudoholomorphic function ω − ω(t, z) in the sense of Bers [1], and α(z) and β(z) are to be chosen suitably.