1.  It must be a weekday, i.e., Monday through Friday.
2.  It must not be during the festal period of one of the great feasts  of  the Lord or the Theotokos.  Such festal periods that fall during the  lesser  fasts are: 
During the Apostles Fast, the Typicon and/or Menaion indicate that  "Alleluia" applies to the following days: 
It was stated in an earlier posting that one can determine if "Alleluia"  is  appointed by checking the Menaion to see whether or not stichera for the  Theotokos are provided in Vespers for "Lord, I have cried."  However,  this  method is not completely accurate.  For example, when a double  commemoration occurs, three stichera are provided for each saint, but  there  are not stichera provided for the Theotokos.  This occurs on the  following  days for which "Alleluia" is indicated: 6 June, 19 November and 15  December.  Also, on 26 November, no stichera for the Theotokos are  provided  in the Menaion, and the Typicon says that stichera from the Octoechos  should be used. 
It should be noted that, besides the simple service or double service to  which "Alleluia" applies, additional services are sometimes also found  in  the Menaion under a particular date.  Usually, these additional services  are to later saints that are venerated in local churches.  If it is  desired  to perform one of these additional services, then the simple or double  service to which "Alleluia" applies is superceded and the Lenten service  is  not performed.  The simple service is usually then read at Compline.
In general, the performing of Lenten services during the three lesser  fasts  is now somewhat rare.  In many places, the Lenten service is only  performed  on the first day of the Apostles and Nativity Fasts.  Occasionally, I  have  seen the Lenten service performed on other days, but such instances have  been more the exception than the rule.  This is a great pity, because we  have become accustomed to observing these fasts without any Lenten  liturgical expression.  This lamentable state of affairs was apparently  recognized at the Pan-Russian Council of 1917-18, and, according to  Bishop  Afanasij (Sakharov), a prominent expert on litrugics, the Council issued  a  decree "concerning the restoration of the practice of performing  services  with alleluia on the appointed days of the lesser fasts."  However, it  is  difficult to say to what extent, if any, this decree was ever implemented.  If anyone has the full text of this decree available, I would be  interested  in hearing from you.
This discussion comes at an opportune time, since we are about to begin  the  Nativity Fast.  It would be most heartening if churches that conduct  daily  services were now to begin serving the "Alleluia" services on the days  appointed during this Fast.  And for those of us who don't have the  opportunity to attend daily services, perhaps we could add the Prayer of  St. Ephraim, with its prostrations and bows, to our Morning and Evening  prayers on those days.
From Reader Daniel Olson - Posted Nov 26, 1998 NS
The "Alleluia" days in the Nativity fast are the following, as marked
in the Typicon, provided they do not fall on a Saturday or Sunday:
 (Dates are Julian): 
From Fr John Shaw
Posted Nov 25, 1998 NS 
Alleluia" days are weekdays in the Fasts on which only three stichera 
for  the day are appointed to be sung on "Lord, I have cried" at Vespers.   
More  importantly, and hence the name, is that also "The Lord is God"
at  Mattins  is replaced by "Alleluia" with its verses (as in
the Great Fast).   In  the  "lesser" Fasts it is common
practice only to observe "Alleluia" days on  Mondays, Wednesdays and
Fridays, although some (as indicated by one  repsonse to my question
concerning the Office of the Typika) suggest  that  they may
be observed on all weekdays.   The fact that only one (or 
perhaps  two) such days are indicated for the Fast of the Dormition
results on  practice in their not being currently generally observed
in that Fast. 
In the longer Fasts of the Apostles and the Nativity rather more days
are indicated for this observance.
"Alleluia" days are usually marked as such in the Great Book of Hours.
Those Saturdays on which the service for the Departed is used are also referred to as "Alleluia" days, but the Lenten form of service is not used.
From Archimandrite Kyril Jenner.
Posted Wed, nove 25, 1998 NS
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