diff --git a/src/parse_time_only_str.rs b/src/parse_time_only_str.rs
index e909216..ef0f814 100644
--- a/src/parse_time_only_str.rs
+++ b/src/parse_time_only_str.rs
@@ -7,11 +7,75 @@ mod time_only_formats {
     pub const TWELVEHOUR: &str = "%r";
 }
 
+/// Convert a military time zone string to a time zone offset.
+///
+/// Military time zones are the letters A through Z except J. They are
+/// described in RFC 5322.
+fn to_offset(tz: &str) -> Option<FixedOffset> {
+    let hour = match tz {
+        "A" => 1,
+        "B" => 2,
+        "C" => 3,
+        "D" => 4,
+        "E" => 5,
+        "F" => 6,
+        "G" => 7,
+        "H" => 8,
+        "I" => 9,
+        "K" => 10,
+        "L" => 11,
+        "M" => 12,
+        "N" => -1,
+        "O" => -2,
+        "P" => -3,
+        "Q" => -4,
+        "R" => -5,
+        "S" => -6,
+        "T" => -7,
+        "U" => -8,
+        "V" => -9,
+        "W" => -10,
+        "X" => -11,
+        "Y" => -12,
+        "Z" => 0,
+        _ => return None,
+    };
+    let offset_in_sec = hour * 3600;
+    FixedOffset::east_opt(offset_in_sec)
+}
+
+/// Parse a time string without an offset and apply an offset to it.
+///
+/// Multiple formats are attempted when parsing the string.
+fn parse_time_with_offset_multi(
+    date: DateTime<Local>,
+    offset: FixedOffset,
+    s: &str,
+) -> Option<DateTime<FixedOffset>> {
+    for fmt in [
+        time_only_formats::HH_MM,
+        time_only_formats::HH_MM_SS,
+        time_only_formats::TWELVEHOUR,
+    ] {
+        let parsed = match NaiveTime::parse_from_str(s, fmt) {
+            Ok(t) => t,
+            Err(_) => continue,
+        };
+        let parsed_dt = date.date_naive().and_time(parsed);
+        match offset.from_local_datetime(&parsed_dt).single() {
+            Some(dt) => return Some(dt),
+            None => continue,
+        }
+    }
+    None
+}
+
 pub(crate) fn parse_time_only(date: DateTime<Local>, s: &str) -> Option<DateTime<FixedOffset>> {
     let re =
         Regex::new(r"^(?<time>.*?)(?:(?<sign>\+|-)(?<h>[0-9]{1,2}):?(?<m>[0-9]{0,2}))?$").unwrap();
     let captures = re.captures(s)?;
 
+    // Parse the sign, hour, and minute to get a `FixedOffset`, if possible.
     let parsed_offset = match captures.name("h") {
         Some(hours) if !(hours.as_str().is_empty()) => {
             let mut offset_in_sec = hours.as_str().parse::<i32>().unwrap() * 3600;
@@ -27,18 +91,33 @@ pub(crate) fn parse_time_only(date: DateTime<Local>, s: &str) -> Option<DateTime
         _ => None,
     };
 
-    for fmt in [
-        time_only_formats::HH_MM,
-        time_only_formats::HH_MM_SS,
-        time_only_formats::TWELVEHOUR,
-    ] {
-        if let Ok(parsed) = NaiveTime::parse_from_str(captures["time"].trim(), fmt) {
-            let parsed_dt = date.date_naive().and_time(parsed);
-            let offset = match parsed_offset {
-                Some(offset) => offset,
-                None => *date.offset(),
-            };
-            return offset.from_local_datetime(&parsed_dt).single();
+    // Parse the time and apply the parsed offset.
+    let s = captures["time"].trim();
+    let offset = match parsed_offset {
+        Some(offset) => offset,
+        None => *date.offset(),
+    };
+    if let Some(result) = parse_time_with_offset_multi(date, offset, s) {
+        return Some(result);
+    }
+
+    // Military time zones are specified in RFC 5322, Section 4.3
+    // "Obsolete Date and Time".
+    // <https://datatracker.ietf.org/doc/html/rfc5322>
+    //
+    // We let the parsing above handle "5:00 AM" so at this point we
+    // should be guaranteed that we don't have an AM/PM suffix. That
+    // way, we can safely parse "5:00M" here without interference.
+    let re = Regex::new(r"(?<time>.*?)(?<tz>[A-IKLMN-YZ])").unwrap();
+    let captures = re.captures(s)?;
+    if let Some(tz) = captures.name("tz") {
+        let s = captures["time"].trim();
+        let offset = match to_offset(tz.as_str()) {
+            Some(offset) => offset,
+            None => *date.offset(),
+        };
+        if let Some(result) = parse_time_with_offset_multi(date, offset, s) {
+            return Some(result);
         }
     }
 
@@ -64,6 +143,17 @@ mod tests {
         assert_eq!(parsed_time, 1709499840)
     }
 
+    #[test]
+    fn test_military_time_zones() {
+        env::set_var("TZ", "UTC");
+        let date = get_test_date();
+        let actual = parse_time_only(date, "05:00C").unwrap().timestamp();
+        // Computed via `date -u -d "2024-03-03 05:00:00C" +%s`, using a
+        // version of GNU date after v8.32 (earlier versions had a bug).
+        let expected = 1709431200;
+        assert_eq!(actual, expected);
+    }
+
     #[test]
     fn test_time_with_offset() {
         env::set_var("TZ", "UTC");