Democrats appear to be making significant gains in some of the nation's most tightly contested congressional races, especially those in economically depressed areas, according to a special Washington Post-ABC News national election poll.

The poll focused on 27 congressional races and shows Democrats ahead in 15 of them, Republicans leading in 11 and one dead heat.

Republicans hold 19 of the 27 seats going into the election, so the net effect, if the poll findings are correct, is that Democrats are on the verge of picking up seven or eight seats in these races alone on Nov. 2.

Political analysts feel Democrats must do well in these races if they are to increase their majority in the House of Representatives by enough seats to counter President Reagan's so-called working majority of Republicans and conservative Democrats, which passed key parts of his economic program. But doing well in these districts alone would not assure such Democratic gains.

Not all signs in the poll are ominous for Republicans. Also included in the special survey were 10 other congressional races. The Democrats are leading in two of three where Democratic and Republican incumbents are facing each other because of redistricting.

But in the other seven, which include five Democratic seats, no incumbent is seeking reelection, and the Republican candidate is ahead in four.

The Post and ABC News interviewed more than 3,100 persons in the 37 districts from Oct. 4-11, or an average of about 84 in each district. Samples that small make it risky to predict the outcome of any one of the 37 races, which is why they have not been individually identified.

But a statistician involved in the project said the probability is extremely high that misreadings of any districts would largely cancel each other and that the results are as valid as political polls generally are.

Among the key findings from the 27 most closely contested races are these:

* Of 12 congressional districts in which Republican incumbents are serving their first term in office, Democrats are leading in six.

* Four districts where Democrats now lead have been held by Republicans for at least the last 10 years; one has been Republican since the turn of the century.

* Republicans lead in only one of eight districts polled that have Democratic incumbents, and in that race the Democrat has been publicly ridiculed because of recent embarrassing incidents.

* As appears to be happening nationally, Democratic voters are supporting their party's candidates to a higher degree than they normally do, and independents are leaning toward Democratic nominees in most of the races.

Districts polled in which Republican incumbents are trailing are spread across the nation, but voters in each share a key characteristic: They tend much more than most Americans to feel that their areas have been among the hardest hit by high unemployment and poor economic conditions.

In most instances, economic statistics show their perceptions to be correct.

Races included among the 27 were chosen because they have been considered by both parties to be extremely close for months. If Republicans can fend off Democrats in these races, it would seem safe to say they should be able to avoid substantial losses in more comfortable Republican districts.

If the Democrats are to register large gains nationally, they must do especially well in these marginal districts. The poll suggests the Democrats rather than the Republicans are passing that first test.

The 1982 House races are considered more important than any in recent years because, if Democrats make substantial gains, they may be able to thwart many of Reagan's programs. Democrats now hold 241 seats in the House and the Republicans 192, with two vacancies.

Most national polls on the congressional campaign ask people only whether they are backing a Republican or Democrat. But, to get people thinking less about partisanship and more about the individual campaigns, Post-ABC interviewers asked people which candidate they were supporting by name in each district.

One of the poll's most striking findings is the extent to which Democratic voters are supporting their party's candidates. Traditionally, the proportion of Democrats supporting Republicans is far higher than the proportion of Republicans supporting Democrats.

In the 37 races included in the poll, however, Republicans are defecting at a slightly higher rate, with 19 percent saying they will vote for the Democrat. Among Democrats, 16 percent say they will vote for the Republican candidate.