The military buildup under President Reagan is notable as much for his tenacity and single-mindedness in promoting it as for the controversial arsenal it has produced.

He promised to ''rearm America,'' and he has presided over the largest peacetime military buildup in United States history. Pentagon spending in Mr. Reagan's first five-year defense plan totaled more than $1.5 trillion, and current plans are closer to $2 trillion. Annual national defense budgets now exceed $300 billion, when nuclear-weapons portions of the Energy Department and military-intelligence funds are included.

The rate of increase in defense funding has surpassed the rest of the federal government by wide margins. And within that sum, the amount dedicated to weapons procurement has jumped at twice the rate of spending for operating and servicing military equipment.

Yet US force structure, as measured in divisions, air wings, and battle groups at sea, is not expanding nearly as much as the dollar figures and weapons stocks would indicate. This is because most of the money is being spent on new tanks, planes, and ships to replace those being retired. In some cases, the ''bow wave'' of new procurement - which inevitably will follow the large down payments already approved by Congress - has yet to occur.

Annual defense spending increases, when adjusted for inflation, averaged about 10 percent during the last 31/2 years. Administration officials say that figure will drop below 5 percent after 1986, when most of the new procurement will have occured.

In 1981, Reagan announced his ''strategic modernization'' program. This included the 10-warhead MX intercontinental ballistic missile (ICBM), the B-1 bomber, new strategic submarines with nuclear missiles, new air defenses, and improvements in the command-and-control structure. Criticism has focused on the MX, which has yet to find a generally accepted basing mode.

The missile has become a symbol of national will and resolve in matching the large Soviet ICBM force. The MX program (which the President calls ''peacekeeper'') may yet be killed by Congress, but so far it continues to survive. The Pentagon also is proceeding with a single-warhead mobile ICBM dubbed ''midgetman,'' which presumably would be less vulnerable to a Soviet first strike and therefore would enhance superpower stability.

Over the next five years, the administration plans to spend some $25 billion on space-based antimissile defenses (dubbed ''star wars'' by opponents).

The Pentagon launched a program to fight waste, abuse, and cost overruns, highlighted by recent spare-parts ''horror stories.'' This crackdown has yielded significant gains. But years of institutional practice among civilian contractors, as well as among uniformed procurement officers, are difficult to change in one or two years, especially when military spending is rising so steeply.

Administration officials say readiness - a subjective indicator that includes morale, the quality of training, and the educational background of new recruits, as well as spare parts and ammunition - is improving. But some new high technology weapons have performed poorly. And some commanders warn that their ammunition stocks remain dangerously low.

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