  The projection method is used to demonstrate the existence of positron
attachment to three doubly excited states of helium. The e^+He(2s^2 1Se),
e^+He(3s^2 1Se), and the e^+He(2s2p 3Po) states have binding energies of
0.447eV, 0.256eV and 0.486eV respectively. These energies were computed with
the stochastic variational method and the configuration interaction method.
These states will exist as resonances in the e^+ + He continuum and the
e^+He(2s^2 1Se) state could be detectable in the e^+ + He collision spectrum. A
resonance width of 0.068eV was computed for the e^+He(2s^2 1Se), state by using
the complex rotation method. The existence of a series of e^+He(ns^2 1Se)
resonances associated with the He(ns^2) double Rydberg series is also predicted
and an explicit calculation demonstrating the existence of the e^+He(3s^2 1Se)
state is reported.
