Very highly excited p states of Cs with principal quantum numbers 30 < or = Eta < or = 85 were produced by one-step photoexcitation with frequency-doubled light from a flash-lamp-pumped dye laser. Field ionization was employed for selective detection. Ionization occurs at field strengths E > or = Emin with a sharp threshold. The relation Emin(n*) varies as (n*)-4 was verified over a wide range. Two-photon excitation to a very high state via a virtual intermediate state leads to immediate ionization of most of the excited atoms; in this case the ion signal as a function of the light intensity I is not proportional to Ik, k > or = 2, whereas a direct two-photon transition into the continuum yields proportionality with Ito the power of 2.