After many decades of cosmic-ray research, the origins of cosmic-ray nuclei are still unknown. Because interstellar magnetic fields deflect charged particles, measurements of the incident directions of cosmic-ray nuclei do not reveal the sites of their production. Therefore, direct evidence of the sites of cosmic-ray acceleration requires detection of neutrally-charged particles, such as gamma rays, produced by the interactions of accelerated cosmic rays with other nuclei near the cosmic-ray accelerators.

It is generally accepted that supernova remnants predominantly accelerate Galactic cosmic rays at least up to energies ~ 100 TeV. No other single known class of objects can explain the properties of the cosmic rays observed at Earth.

Pulsars may accelerate some fraction of the galactic cosmic-ray electrons and nuclei. Pulsars are observed to accelerate particles to energies of at least ~ 1 TeV and are the strongest galactic gamma-ray sources at these energies and at energies ~ 100 MeV.

This thesis describes searches for evidence of gamma-ray emission from five supernova remnants and from the Geminga pulsar at energies ~ 100 TeV using the data set of the CYGNUS-I extensive air-shower array.

The analyses of the five supernova remnants, which are positionally coincident with gamma-ray sources observed with the EGRET detector at energies 100 MeV, reveal no evidence of gamma-ray emission at energies ~ 100 TeV. A comparison of the gamma-ray flux upper limits from the CYGNUS-I data to the fluxes measured with the EGRET instrument suggests that the integral cosmic-ray spectra of the five supernova remnants may soften by about 100 TeV or may be steeper than an E^-1.3 power-law distribution.

The analysis of the Geminga pulsar reveals no evidence of either pulsed or unpulsed gamma-ray emission from this object at energies ~ 100 TeV. This result is consistent with present models of particle acceleration by pulsars.