diff --git a/Ical.Net.Tests/contrib/libical/icalrecur_test.out b/Ical.Net.Tests/contrib/libical/icalrecur_test.out
index 87e3cbc73..8d957baef 100644
--- a/Ical.Net.Tests/contrib/libical/icalrecur_test.out
+++ b/Ical.Net.Tests/contrib/libical/icalrecur_test.out
@@ -340,11 +340,10 @@ DTSTART:20190101T100000
 INSTANCES:20190102T100000,20190104T100000,20190116T100000,20190118T100000
 PREV-INSTANCES:20190116T100000,20190104T100000,20190102T100000
 
-# TODO: FIX (see https://github.com/ical-org/ical.net/issues/618)
-# RRULE:FREQ=YEARLY;BYWEEKNO=1,2,-1,-2;BYDAY=TU;UNTIL=20170101T000000Z
-# DTSTART:20130101T000000
-# INSTANCES:20130101T000000,20130108T000000,20131217T000000,20131224T000000,20131231T000000,20140107T000000,20141216T000000,20141223T000000,20141230T000000,20150106T000000,20151222T000000,20151229T000000,20160105T000000,20160112T000000,20161220T000000,20161227T000000
-# PREV-INSTANCES:20161227T000000,20161220T000000,20160112T000000,20160105T000000,20151229T000000,20151222T000000,20150106T000000,20141230T000000,20141223T000000,20141216T000000,20140107T000000,20131231T000000,20131224T000000,20131217T000000,20130108T000000,20130101T000000
+RRULE:FREQ=YEARLY;BYWEEKNO=1,2,-1,-2;BYDAY=TU;UNTIL=20170101T000000Z
+DTSTART:20130101T000000
+INSTANCES:20130101T000000,20130108T000000,20131217T000000,20131224T000000,20131231T000000,20140107T000000,20141216T000000,20141223T000000,20141230T000000,20150106T000000,20151222T000000,20151229T000000,20160105T000000,20160112T000000,20161220T000000,20161227T000000
+PREV-INSTANCES:20161227T000000,20161220T000000,20160112T000000,20160105T000000,20151229T000000,20151222T000000,20150106T000000,20141230T000000,20141223T000000,20141216T000000,20140107T000000,20131231T000000,20131224T000000,20131217T000000,20130108T000000,20130101T000000
 
 RRULE:FREQ=YEARLY;BYWEEKNO=53;BYDAY=TU,SA;UNTIL=20170101T000000Z
 DTSTART:20130101T000000
diff --git a/Ical.Net/CalendarExtensions.cs b/Ical.Net/CalendarExtensions.cs
index 6848ef293..8b0007f47 100644
--- a/Ical.Net/CalendarExtensions.cs
+++ b/Ical.Net/CalendarExtensions.cs
@@ -39,4 +39,34 @@ private static DateTime GetStartOfWeek(this DateTime t, DayOfWeek firstDayOfWeek
         var tn = ((int) t.DayOfWeek) % 7;
         return t.AddDays(-((tn + 7 - t0) % 7));
     }
+
+    /// <summary>
+    /// Calculate the year, the given date's week belongs to according to ISO 8601, as required by RFC 5545.
+    /// </summary>
+    /// <remarks>
+    /// A date's nominal year may be different from the year, the week belongs to that the date is in.
+    /// I.e. the first and last week of the year may belong to a different year than the date's year.
+    /// E.g. for `2019-12-31` with first day of the week being Monday, the method will return 2020,
+    /// because the week that contains `2019-12-31` is the first week of 2020.
+    /// </remarks>
+    public static int GetIso8601YearOfWeek(this System.Globalization.Calendar calendar, DateTime time, DayOfWeek firstDayOfWeek)
+    {
+        var year = time.Year;
+        if ((time.Month >= 12) && (calendar.GetIso8601WeekOfYear(time, firstDayOfWeek) == 1))
+            year++;
+        else if ((time.Month == 1) && (calendar.GetIso8601WeekOfYear(time, firstDayOfWeek) >= 52))
+            year--;
+
+        return year;
+    }
+
+    /// <summary>
+    /// Calculate the number of weeks in the given year according to ISO 8601, as required by RFC 5545.
+    /// </summary>
+    public static int GetIso8601WeeksInYear(this System.Globalization.Calendar calendar, int year, DayOfWeek firstDayOfWeek)
+    {
+        // The last week of the year is the week that contains the 4th-last day of the year (which is the 28th of December in Gregorian Calendar).
+        var testTime = new DateTime(year + 1, 1, 1, 0, 0, 0, DateTimeKind.Unspecified).AddDays(-4);
+        return calendar.GetIso8601WeekOfYear(testTime, firstDayOfWeek);
+    }
 }
diff --git a/Ical.Net/Evaluation/RecurrencePatternEvaluator.cs b/Ical.Net/Evaluation/RecurrencePatternEvaluator.cs
index 118bdbc0d..376332467 100644
--- a/Ical.Net/Evaluation/RecurrencePatternEvaluator.cs
+++ b/Ical.Net/Evaluation/RecurrencePatternEvaluator.cs
@@ -395,7 +395,7 @@ private List<DateTime> GetWeekNoVariants(List<DateTime> dates, RecurrencePattern
         var weekNoDates = new List<DateTime>();
         foreach (var t in dates)
         {
-            foreach (var weekNo in pattern.ByWeekNo)
+            foreach (var weekNo in GetByWeekNoForYearNormalized(pattern, t.Year))
             {
                 var date = t;
                 // Determine our current week number
@@ -429,6 +429,17 @@ private List<DateTime> GetWeekNoVariants(List<DateTime> dates, RecurrencePattern
         return weekNoDates;
     }
 
+    /// <summary>
+    /// Normalize the BYWEEKNO values to be positive integers.
+    /// </summary>
+    private List<int> GetByWeekNoForYearNormalized(RecurrencePattern pattern, int year)
+    {
+        var weeksInYear = new Lazy<int>(() => Calendar.GetIso8601WeeksInYear(year, pattern.FirstDayOfWeek));
+        return pattern.ByWeekNo
+            .Select(weekNo => weekNo >= 0 ? weekNo : weeksInYear.Value + weekNo + 1)
+            .ToList();
+    }
+
     /// <summary>
     /// Applies BYYEARDAY rules specified in this Recur instance to the specified date list. 
     /// If no BYYEARDAY rules are specified, the date list is returned unmodified.
@@ -641,13 +652,14 @@ private List<DateTime> GetAbsWeekDays(DateTime date, WeekDay weekDay, Recurrence
 
             var nextWeekNo = Calendar.GetIso8601WeekOfYear(date, pattern.FirstDayOfWeek);
             var currentWeekNo = Calendar.GetIso8601WeekOfYear(date, pattern.FirstDayOfWeek);
+            var byWeekNoNormalized = GetByWeekNoForYearNormalized(pattern, Calendar.GetIso8601YearOfWeek(date, pattern.FirstDayOfWeek));
 
             //When we manage weekly recurring pattern and we have boundary case:
             //Weekdays: Dec 31, Jan 1, Feb 1, Mar 1, Apr 1, May 1, June 1, Dec 31 - It's the 53th week of the year, but all another are 1st week number.
             //So we need an EXRULE for this situation, but only for weekly events
             while (currentWeekNo == weekNo || (nextWeekNo < weekNo && currentWeekNo == nextWeekNo && pattern.Frequency == FrequencyType.Weekly))
             {
-                if ((pattern.ByWeekNo.Count == 0 || pattern.ByWeekNo.Contains(currentWeekNo))
+                if ((byWeekNoNormalized.Count == 0 || byWeekNoNormalized.Contains(currentWeekNo))
                     && (pattern.ByMonth.Count == 0 || pattern.ByMonth.Contains(date.Month)))
                 {
                     days.Add(date);
@@ -668,11 +680,12 @@ private List<DateTime> GetAbsWeekDays(DateTime date, WeekDay weekDay, Recurrence
                 date = date.AddDays(1);
             }
 
+            var byWeekNoNormalized = GetByWeekNoForYearNormalized(pattern, Calendar.GetIso8601YearOfWeek(date, pattern.FirstDayOfWeek));
             while (date.Month == month)
             {
                 var currentWeekNo = Calendar.GetIso8601WeekOfYear(date, pattern.FirstDayOfWeek);
 
-                if ((pattern.ByWeekNo.Count == 0 || pattern.ByWeekNo.Contains(currentWeekNo))
+                if ((byWeekNoNormalized.Count == 0 || byWeekNoNormalized.Contains(currentWeekNo))
                     && (pattern.ByMonth.Count == 0 || pattern.ByMonth.Contains(date.Month)))
                 {
                     days.Add(date);