  We investigate theoretically and experimentally the optical second harmonic
generation (SHG) with a twisted Gaussian Schell model (TGSM) beam as the
fundamental field. We use Type-II phase matching and analyze the cross spectral
density (CSD) of the SHG output beam when the input fundamental is prepared
with a TGSM structure. We analyze two synthetization methods for preparing the
TGSM fundamental beam and we find that for one method the SHG is also a TGSM
beam. For the other method, we find that the SHG is not a TGSM beam and
presents an anomalous CSD possessing a dip instead of a peak in the transverse
spatial structure. Moreover, we show that the dip depth is directly related to
the twisted phase parameter, being absent for a non twisted GSM beam. Our
results show that the SHG from a fundamental TGSM beam can result in a doubled
frequency TGSM or in a non-TGSM beam depending on the synthetization method.
