Aliturgic

Better indeed would it be to return to the old Jewish sacrifices, than to embrace the aliturgic weakness of Protestantism.

Source: wiktionary

It is probable that the custom of reserving for the aliturgic days, and permitting the people to communicate of the presanctified, i.e. the previously consecrated, gifts, in order to satisfy this desire, arose in the Greek Church not later than the earlier part of the seventh century.

Source: wiktionary

Saturday in Holy Week marked the rest of Christ in the tomb and was a totally aliturgic day with a total fast. The Eucharist was not celebrated.

Source: wiktionary

This is done on Maundy Thursday, and the particles so treated serve for the aliturgic days of Lent, and for the sick.

Source: wiktionary