Using data from inclined events ( 60 degrees <straight theta<80 degrees ) recorded by the Haverah Park shower detector, we show that above 10(19) eV less than 41% ( 54%) of the primary cosmic rays can be photons (iron nuclei) at the 95% confidence level. Above 4x10(19) eV less than 65% of the cosmic rays can be photonic at the same confidence level. These limits place important constraints on some models of the origin of ultrahigh-energy cosmic rays. Details of two new events above 10(20) eV are reported.