Only one third of American family members feel that things in this country are going well today, according to a new national survey, but virtually all feel that things are going well for their families.

This finding highlights the curious mixture of optimism and pessimism presented in "Families at Work: Strengths and Strains," sponsored by General Mills, Inc., and conducted by the research firm of Louis Harris and Associates.

The report is the fourth survey in a series of "family attitude" studies General Mills has presented since 1975. It is based on interviews with six different groups: a national cross section of 1,503 adult family members, 235 teen-agers, 104 "human resource executives" from Fortune 1,300 companies, 56 labor leaders, 49 "family traditionalists" and 52 feminists.

"The survey points with assurance to one indisputable fact," Harris' deputy chairman Humphrey Taylor said at a press conference last week: "A majority of women want to and will continue to work outside the home -- marriage and child-rearing responsibilities notwithstanding.

"The past 10 years have established a pattern for the future of families at work. More than 5 out of 10 women living in families are now employed outside the home. Most of these women are married. Most have children under the age of 18 at home."

Although Taylor said "attitudes about women working -- and about the job of homemaking -- have undergone profound changes," some of these new attitudes seem to conflict.

On the one hand: "The feeling now dominant in the land is that it is best, and healthiest, for women to work -- even if the family doesn't need the money."

On the other: "According to most family members, the trend toward both parents working outside the home has had negative effects on families. The reason most often cited is that 'children need stronger parental guidance, supervision and discipline' than can be given when both parents work."

So it comes as no surprise to learn that "working mothers bear particular burdens and pressures," and that "findings throughout the study delineate the conflicts facing women as wives, mothers and wage earners."

For example: "Overwhelming majorities of both family members and leaders recognize that it's more difficult for women to get ahead in a career job because family responsibilities usually fall on them."

And "while two in three family members say they do have enough time for themselves -- and one in two working women agree -- it is working mothers who say they do not, by 63 percent to 36 percent."

The benefits of work, according to family members, include a better standard of living, a higher feeling of accomplishment and the ability to affords a home, provide for necessities and educate children.

The strains of work include lack of time with family/children, long hours and pressure, not having enough leisure time and not making enough money.

In weighing pros and cons, Taylor noted, "most feminists and many working mothers, feel that the fulfillment for women working outside the home, the added financial security, improved family communications and independence for children outweigh the negatives."

But, not surprisingly, family traditionalists (defined as leaders in the "pro-family" movement) disagreed. They unanimously stated that the trend toward both parents working outside the home has had "a generally negative effect" on families.

Teen-agers also voiced a mixture of optimism and pessimism about having both parents work -- depending on the age of the child. Fifty-four percent said they felt the trend toward mothers, and fathers working outside the home has had "generally bad effects on children 12 years and under." But for teen-agers, they said having both parents work has "generally good effects" (33 percent) or "no effects at all" (37 percent).

While 81 percent of teen-agers whose parents both work and their mothers spend an adequate amount of time with them, only 60 percent said the same about their fathers.

Although Taylor said "family members resist efforts to prescribe a single solution to the conflicting demands of work and family responsibilities," he added that "there is a gread demand for recognition by employers of their needs and concerns and for more understanding in working out approaches to meet them. There is a clear call for compromise. The workplace will have to bend."

Among the policies corporation leaders said their organizations have adopted are: the right to resume work at the same pay and seniority after a personal leave of absence (60 percent); the right to refuse relocation or transfer with no career penalty (48 percent); a shorter work week with less pay (34 percent), and a choice of flexible hours (28 percent).