Employes of the General Services Administration have awarded hundreds of thousands of dollars in contracts for the repair and alteration of federal buildings here to nonexistent companies and companies that do not perform the work paid for extensive investigaions by the GSA and the FBI have found.

Sources familiar with the investigation said the contract fraud has been going on for many years and may have been passed from one generation of GSA employes to the next.

Investigators have yet to trace money back to any GSA employe.They pointed out that anyone connected with the paying or receiving of government money for work not performed is liable to criminal prosecution.

A federal grand jury here has issued subpoenas for GSA contracts and other documents extending over the past several months to further the investigation here, and the FBI has broadened its investigation to federal contract awards by other agencies and in other cities.

The General Services Administration awards contracts for the construction, leasing and repairing of government offices, and for purchasing government supplies. GSA spends $4.5 billion a year, including nearly $250 million to repair, alter and operate federal buildings in the Washington area.

Managers of these buildings have authority to award individual repair and alteration contracts, often without competitive bidding, in amounts of $10,000 or less. A number of the suspected fraudulent contracts are of this type, the sources said, although others involve larger amounts.

The alleged fraud has taken a number of forms, according to the sources familiar with the investigation: one scheme involves awarding and paying for a contract for two costs of paint when only one was needed and applied; another involved contracting to install 20,000 square feet of tile on a 10,000-square-foot floor.

In some cases, contracts have been awarded to a private firm when the work has actually been performed by GSA employes. In other cases, several contracts have been awarded to perform a single job -- such as installation of new tile -- over a span of several years.

In one instance, GSA contracted to paint a wall seven times in five years. Laboratory tests on the layers of paint determined that most of the costs contracted for had never been applied.

The contracts have been awarded either to legitimate contracting firms or to "shell" companies with private residences as addresses. One company receiving contracts consisted of two former GSA employes, according to sources.

Some of the companies have received hundreds of contracts over several years to perform work on only a single building, the sources said.

The millions of dollars in fradulent contracts uncovered so far were awarded over the past five years. Investigators have been hampered in probing over a longer period because records have been routinely destroyed.

The investigators also have encountered sloppy record-keeping practices. In some instances, it is difficult to trace the individual responsible for awarding a contract because many officials appear to have approved each contract. In addition, GSA apparently has no index of contracts awarded.

The fraudulent contracting practices were uncovered when a GSA employe in Chicago was convicted in 1976 for awarding fraudulent repair contracts. GSA assigned a task force eventually numbering as many as 100 auditors and investigators to look for the same abuses in other cities. They found most of the fraudulent contracts in GSA's Region 3, which covers the Washington area. This also buildings are located. It is not known how many of the hundreds of employes in the region who have a role in contract awards are involved in the investigation.

Last year, GSA turned over its findings to the FBI, which has been pursuing the case aggressively.

The outcome of the investigation is expected to influence a current assessment of GSA by a government reorganization team. The team is evaluating how well GSA performs and whether its functions should be expanded or diminished.