Did John Bunyan believe in predestination and irresistible grace? This particular question is concerned with John Bunyan's stance, rather than the stance of Pilgrim's Progress, which is addressed in a related question.

I learned of Pilgrim's Progress through reading works of reformed theologians (many of who highly recommended Pilgrim's Progress), and thus I assumed that Pilgrim's Progress also believed in predestination.  I'm no longer sure of that, and I'm not even sure if John Bunyan himself believed in predestination. (Wikipedia doesn't seem to say either way)

Thus, the question: did John Bunyan take a stance on predestination and irresistible grace?
It's clear from the writings of John Bunyan that he believed in the Reformed doctrines of predestination and irresistible grace.  He makes an extensive defense of these and related doctrines in his work, Come and Welcome to Jesus Christ, in which he analyzes John 6:37:

All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out. [KJV]

Demonstrating his belief in predestination, he writes that the &quot;all&quot; of this verse are the elect:

Those, therefore, intended as the gift in the text, are those that are given by covenant to the Son; those that in other places are called “the elect,” “the chosen,” “the sheep,” and “the children of the promise,” &amp;c. These be they that the Father hath given to Christ to keep them; those that Christ hath promised eternal life unto; those to whom he hath given his word, and that he will have with him in his kingdom to behold his glory. (5; 8)

He sees the &quot;giving&quot; of this verse as not only something happening in the present, with the transformation of individual sinners, but also something that God did long ago:

this gift was bestowed upon Christ when the covenant, the eternal covenant, was made between them before all worlds. (6; 11)

Turning now to the doctrine of irresistible grace, we see that Bunyan also clearly teaches it in this work.  He spends many pages expounding on the &quot;shall come&quot; of John 6:37, arguing that it is an absolute promise of God that cannot be circumvented by anything, not even the will of man:

The Father’s end was, that they might come to him, and be saved by him; and that, says the Son, shall be done; neither sin nor Satan, neither flesh nor world, neither wisdom nor folly, shall hinder their coming to me. (9; 19)

But what of the one who insists that he will not be saved?  Is it possible for him to resist God's will?  Bunyan says no:

Here, then, is the case; we must now see who will be the liar, he that saith, &quot;I will not&quot;; or he that saith, &quot;He shall come to me.&quot; &quot;You shall come,&quot; says God; &quot;I will not come,&quot; saith the sinner. Now, as sure as he is concerned in this Shall-come, God will make that man eat his own words; for &quot;I will not,&quot; is the unadvised conclusion of a crazy-headed sinner; but Shall-come was spoken by him that is of power to perform his word. [bold and quotation marks added] (22; 51)

How will this be done?  Will such people be dragged into the kingdom against their will?  On the contrary, says Bunyan:

The obstinacy and plague that is in the will of that people, shall be taken away; and they shall be made willing; Shall-come will make them willing to come to thee. (22; 52)

Summary
John Bunyan's formulations of predestination and irresistible grace do not diverge from the historical teaching of the Reformed faith.  It's true that he differed with Calvinists on some matters related to ecclesiology and the sacraments, but his understanding of salvation corresponds neatly with theirs.

Quotes come from Come and Welcome to Jesus Christ, a PDF published by bunyanministries.org.  The first number after each quote indicates the page number in that edition.  The second number after each quote refers to the page number in a 1774 edition of this work.