(FORTUNE Magazine) – "You like me! You really like me!" No, it's not Sally Field. It's the gushing of an electrical engineer attending the Westech Career Expo, a job fair for hardware and software engineers. The June Westech in Santa Clara, Cal., filled a convention center in the heart of Silicon Valley with the booths of 416 eager employers--wall-to-wall smiles--whose desperation to fill thousands of vacant positions was painfully palpable. Qualified job seekers had only to heed this advice: "Go hire yourself an employer!"

Take your pick: Over here is disk-drive maker Quantum Corp., hoping this year to fill 2,000 positions, like VLSI CAD engineer; over there is Cisco Systems, upon whose counter sits a telephone-book-sized directory filled with descriptions of the 400 positions open at this very moment. Startups abound--just stick out your hand for that 1% equity slice as a signing bonus. Then there's Apple Computer. Its booth features a poster of a bicyclist on a tightrope, and text that seeks to turn the company's woes into an Extreme Sports attraction: "There will always be disbelievers. There will always be Apple to prove them wrong."

Everything about Westech is designed to woo engineers, who could hardly be in greater demand. Stephen Levy, an economist at the Center for Continuing Study of the California Economy, in Palo Alto, estimates that the unemployment rate for technical specialties is 1% or lower. That's pure frictional unemployment--a snapshot of engineers who happen to be crossing the parking lot after quitting company A to join company B. Since everyone has a job, Westech is open only at lunchtime and in the late afternoon and early evening. To entice applicants to appear in person rather than merely fax or E-mail a resume, astute employers send hiring managers to Westech, not powerless functionaries from human resources. Hewlett-Packard alone brought 80 managers, who fielded 4,000 resumes in the course of two days.

Applicants walk up, slap a resume on the counter, and while the manager reads it, deliver a 60-second spiel. It's not likely an offer will be made on the spot--the esoteric nature of the specialties necessitates fuller interviews back at the office (Quantum, for example, is hungry for "tribologists," experts in the effects of friction on moving machine parts). But these quick, personal encounters greatly speed up the mating dance.

Westech has been a Silicon Valley institution since the early 1980s, and now can be found as a roving institution in other cities. Its bimonthly Santa Clara fair is the largest, and June's ran at full capacity. The fair thrives on the acute mismatch between the enormous demand for, and the inadequate supply of, well-qualified technical personnel. That mismatch can be explained to some extent as the inevitable tightness to be expected during the continuing expansion of the economy. Also, many Westech companies are busy trying to make up for lost time. As their industries' prospects brightened after difficulties in the early 1990s, they held off staffing up for growth so as to avoid layoffs down the road. The downturn never came, so now they're desperate.

Other aspects of the present situation are more subtle. On the demand side, it is interesting to note that frantic though employers may be, they are also just as picky as ever. Typical is the company that asks for people who can write applications for Java, NT, Unix, and C++; not any one of those, but all of the above. Companies also prize three to five years' experience. Newly minted graduates or those with long, long experience in industry (such as those who cut their teeth on Cobol in the Pleistocene Epoch) require on-the-job training. Training requires time, and time is what these companies lack most of all.

You might think that when employers clamor to outbid each other for the services of an engineering elite, the gap between the gearheads and the unlucky majority of the local labor market would open into a Grand Canyon-sized chasm. Actually it hasn't, at least not so far. Silicon Valley's retail sector is booming, thanks to spillover from high tech's prosperity. The local unemployment rate dropped to 3.1% in May.

Still, engineers are in the highest demand. A decent argument can be made that Silicon Valley's present boom is more than just cyclical efflorescence: that it reflects the diffusion of electronics into ever more nooks and crannies of the economy; that it also reflects the digitization of communications; and that these trends will not disappear and the need for newly trained engineers will remain strong. So why not crank out more of these guys and make life a little easier for employers?

Not so easy to do. A university cannot "ramp up" the way a company expands production. The hiring of engineering faculty involves recruiting from the same pool in which private industry is fishing with larger, sweeter bait. University boards are also reluctant to dramatically expand faculty ranks on the basis of today's hot market. They don't simply hire someone; they award tenure, the assurance of lifetime employment. So it's not surprising that they measure time in decades, not fiscal quarters.

If there is a business downturn, students who were about to begin engineering programs will flee. Explains Don Kirk, San Jose State University's dean of engineering: "Students make decisions on the basis of what they see when they enter." The class of '97 is composed of the hardy souls who entered in 1993 and stuck with engineering during the dark days when demand was weak. Nationally the number of bachelor's degrees awarded in electrical engineering and computer science peaked in 1987.

The number has gone down each year since then. Applications to Silicon Valley's engineering schools reflect the national trend, which creates a particularly vexing problem. Employers can't easily make up for the local shortfall, in part because imported young talent faces an area with a frightfully high cost of living.

Given these factors, it's unlikely that employers will get a work force the size and quality they'd like for many years. One added worry: In 1995, the most recent year for which national data are available, only 8.9% of bachelor's degrees in engineering were awarded to women. This is less an issue of political correctness than one of national competitiveness. The underrepresentation of women in engineering (evident to even the casual visitor to Westech) contributes directly to the shortage of engineers that hobbles U.S. companies in the fastest-moving portion of the nation's economy. Sure, the present labor market is paradise for job hunters; but it's hell for employers, and it's unlikely to get better anytime soon.

INSIDE: Great summer gizmos from Motorola and Koss, page 102... Why Xerox watches how employees use the intranet, page 103... Alsop on big ideas for venture capitalists, page 106...