Using ～なければいけません, we will say what we have to do this week. This construction replaces the い in the short form negative tense, and it can also be combined with other verbs to express the idea of ‘I think I have to do something’ or ‘he said he has to do something’ and so on.

We will say that this week we have to go to the library and make dinner for our mother:
A：今週図書館に行かなければいけません。（今しゅうと書かんに行かなければいけません。）
B:　今週母に晩ご飯を作らなければいけません。（今しゅう母にばんごはんを作らなければいけません。）

Using ～なければいけませんでした, we will say what we had to do yesterday. This construction replaces the い in the short form negative tense, and it can also be combined with other verbs to express the idea of ‘I think I have to do something’ or ‘he said he has to do something’ and so on.

We will say that yesterday we had to study and go to a friend’s party:
A：昨日、勉強しなければいけませんでした。
B:　昨日、友達のパーティーに行かなければいけませんでした。（きのう、友だちのパーティーに行かなければいけませんでした。）