How to detect if a date is within this or next week in java?

It partly depends on what you mean by "this week" and "next week"... but with Joda Time it's certainly easy to find out whether it's in "today or the next 7 days" as it were:

LocalDate event = getDateFromSomewhere();
LocalDate today = new LocalDate();
LocalDate weekToday = today.plusWeeks(1);
LocalDate fortnightToday = weekToday.plusWeeks(1);

if (today.compareTo(event) <= 0 && event.compareTo(weekToday) < 0)
{
    // It's within the next 7 days
}
else if (weekToday.compareTo(event) <= 0 && event.compareTo(fornightToday) < 0)
{
    // It's next week
}

EDIT: To get the Sunday to Saturday week, you'd probably want:

LocalDate startOfWeek = new LocalDate().withDayOfWeek(DateTimeConstants.SUNDAY);

then do the same code as the above, but relative to startOfWeek.

How about this :

Calendar c=Calendar.getInstance();
c.set(Calendar.DAY_OF_WEEK,Calendar.SUNDAY);
c.set(Calendar.HOUR_OF_DAY,0);
c.set(Calendar.MINUTE,0);
c.set(Calendar.SECOND,0);
DateFormat df=new SimpleDateFormat("EEE yyyy/MM/dd HH:mm:ss");
System.out.println(df.format(c.getTime()));      // This past Sunday [ May include today ]
c.add(Calendar.DATE,7);
System.out.println(df.format(c.getTime()));      // Next Sunday
c.add(Calendar.DATE,7);
System.out.println(df.format(c.getTime()));      // Sunday after next

The result :

Sun 2010/12/26 00:00:00
Sun 2011/01/02 00:00:00
Sun 2011/01/09 00:00:00

Any day between the first two is this week, anything between the last two is next week.

Although old question - is still relevant. The most upvoted answer here is correct wrt to Joda-time and wrt to JDK8 as well with some syntax changes. Here's one that might help those who are looking around in JDK8 world.

 public static boolean isLocalDateInTheSameWeek(LocalDate date1, LocalDate date2) {
    LocalDate sundayBeforeDate1 = date1.with(TemporalAdjusters.previousOrSame(DayOfWeek.SUNDAY));
    LocalDate saturdayAfterDate1 = date1.with(TemporalAdjusters.nextOrSame(DayOfWeek.SATURDAY));
    return  ((date2.isEqual(sundayBeforeDate1) || date2.isAfter(sundayBeforeDate1)) 
            && (date2.isEqual(saturdayAfterDate1) || date2.isBefore(saturdayAfterDate1)));
}