Even as women moved into men’s jobs, in fields like medicine, law and business, men did not flock to the lower-status jobs that women mostly did.

That’s changing. Over the last 15 years, according to a new study, men have been as likely to move into predominantly female jobs as the other way around — but not all men. It’s those who are already disadvantaged in the labor market: black, Hispanic, less educated, poor and immigrant men. While work done by women continues to be valued less, the study demonstrates, job opportunities divide not just along gender lines but also by race and class.

At the same time, the women who have continued to make inroads into more prestigious male-dominated professions in that period are likely to be white, educated, native-born and married, according to the research, which is not yet published. “More privileged men can resist entry into predominantly female occupations more readily than their less privileged counterparts,” said Patricia A. Roos, a sociologist at Rutgers, who did the study with Lindsay M. Stevens, a sociology doctoral student there.

The gender composition of jobs matters for reasons of equality — fields with a majority of men pay 21 percent more than those with mostly women. Also, the fastest-growing jobs are dominated by women, while the fastest-shrinking ones are predominately male.