An observation of horizontal air showers has been continued during these four years with the air shower array at the Institute for Nuclear Study, University of Tokyo. The integral size spectrum is expressed by (4.9±0.7)×10 -13 ( N /10 4 ) -2.8±0.3 cm -2 sec -1 ster -1 for the showers of sizes 10 3 to 10 5 and zenith angles above 70°. The zenith angle distributions for three size regions (0.5∼1)×10 4 , (1∼2)×10 4 and (2∼4)×10 4 indicate that the intensities are proportional to sec θ from 60° to 75° and decrease at above 75°±5° with attenuation mean free path of 5,000 to 10,000 g/cm 2 . The proportion of nuclear cascade showers to the total showers is estimated to be (20∼70)% in the range of size 3×10 3 to 6×10 4 . The implications of an effect of possible anomalous muon interactions and of, as an alternative, a possibility of heavy mass particles being the parent particles of the horizontal air showers are discussed.