Police departments, oil rig operators, cellular mobile telephone companies and airline telephone service firms are pressuring the Federal Communications Commission to give them more room on the airwaves by allocating new space or squeezing more out of the space that exists.

The demand for use of public-safety two-way radio communications systems and other mobile radio services is growing exponentially, the agency said, and it is working on a technical solution to the space shortage as well as trying to decide who should get a limited amount of untouched reserve space. Decisions on those issues aren't expected for a number of months.

"There is reserve spectrum, and cellular phones are competing with land mobile satellite systems that would reach every corner of the nation," said Robert Powers, the FCC's chief scientist. "Other contenders for the limited space are air-to-ground telephone service and the public safety community. All of these communities are vying for that spectrum and it is complicated."

Cellular telephone service uses radio transmitters to power mobile telephones, and land mobile satellite technologies use satellites to send signals that power two-way radio systems instead of conventional ground transmitters.

Congress has asked the agency to "consider very carefully the needs of the land mobile safety people" such as police departments, fire departments and other disaster control agencies, Powers said.

Even so, the agency has concluded "the public safety people need more spectrum than the commission is likely to find," Powers said. The remaining solutions include "taking spectrum away from people now using it or learning to use the spectrum in a far more efficient way."

The commission is encouraging the development of technologies that allow more conversations to fit on radio channels and new technologies that will make it possible for police and fire departments using different equipment to "talk" on the same frequencies. "Something hits the 14th Street bridge and everybody would like to communicate with each other," he said.

One important proposal would involve letting land mobile communications services share the UHF television station spectrum used by TV channels 14 through 20. The agency is trying to iron out technical problems to decrease the chance of interference on television sets.

The most glaring problem, though, is who is going to pay for these technologies. "That is the issue -- who takes care of the technology?" said Powers.

STATION SWAP . . . The FCC has been barraged with comments from broadcasters and other organizations, asking the commission not to bless the "swapping" of educational and commercial television stations. The agency is considering whether to let commercial television stations operating on the UHF band (Channels 14 through 69) swap with noncommercial stations operating on the more desirable VHF frequencies (channels 2 through 13) in exchange for cash. Broadcasters say the proposal would leave educational stations with an inferior signal and smaller audience, discouraging funding of public television. Should the Mass Media Bureau recommend the action, about 300 educational stations could swap their VHF channels.

MILESTONES . . . William F. Adler has become acting deputy bureau chief of operations for the Common Carrier Bureau, after serving as deputy bureau chief for policy since August 1983. Carl D. Lawson has been named acting deputy bureau chief of policy after serving as special assistant to the bureau chief since October 1984.