At one of his dinner parties, Dr. Jekyll is confronted by a concerned Mr. Utterson regarding his will and the character of Mr. Hyde. When Utterson states that he's heard "abominable" things about Hyde, Jekyll says,

You do not understand my position . . . . I am painfully situated, Utterson; my position is a very strange—a very strange one. It is one of those affairs that cannot be mended by talking.

Thus, Jekyll has a kind of external conflict with Utterson, only because Utterson is looking out for the doctor's best interests and Jekyll does not want to reveal the particulars of his situation and relationship with Hyde (for obvious reasons). This line, however, also shows a bit about his internal conflict as well. It is "painful" for him to be in the position he's in: at this point, he must already fear that Hyde could take over (as he's made provisions for this in his will, and he extracts an additional promise from the lawyer that, in the event of Jekyll's disappearance, Utterson will help "get his rights for him").

Jekyll also has an external conflict with Dr. Lanyon, who Jekyll calls "'a hide-bound pedant," an "ignorant, blatant pedant" in whom Jekyll declares he has never been more disappointed. Later, Utterson learns of a complete falling-out between the two old friends, and a short while after this, Lanyon actually dies from some shock. Utterson eventually learns the history of how this happened after both men are dead.

With The Strange Case of Dr. Jekyll and Mr. Hyde, the main external conflict is one Utterson is faced with: the mystery of the relationship between Dr. Jekyll and Mr. Hyde and its impact on others. Fitting into this conflict are the fates of Dr. Lanyon, who dies from the shock of the truth, and a Member of Parliament, Sir Danvers Carew, who is murdered by Hyde. These events are external consequences of the internal conflict Jekyll suffers as he pursues the creation and, later, the destruction of his alter ego.

Jekyll’s internal conflict is laid out for the reader in the final chapter, when one finally gets to read from the man himself his justifications and the means by which he created this evil, villainous side of himself that lived in the dingiest parts of London and violently trod over little girls late at night.

Another internal conflict that the reader is more familiar with is that which Utterson experiences. Acting as Jekyll’s lawyer, he is in possession of the mysterious will, which leaves everything to Hyde in the event of the man’s disappearance. For most of the text, Utterson suspects foul play, perhaps blackmail. He tries to warn his friend and tries to comfort him, but he is not allowed to understand the full details of the case, and he spends most of the novella worrying for the poor Doctor and wondering if there’s anything else he could be doing.

In Robert Louis Steveson's story, The Strange Case of Dr. Jekyll and Mr. Hyde, I believe that Dr. Jekyll is greatly conflicted about what he has done.

In terms of the internal conflict, Dr. Jekyll lives each day knowing that when he is Mr. Hyde, he is doing terrible things. Attack and then murder are things that come from Mr. Hyde, but Jekyll is partly responsible if not in the choice to carry out these actions, then from providing the opportunity that Mr. Hyde can. His sense of guilt would be man vs. self.

An external conflict is that which exists between the authorities trying to make sense of Hyde's actions and track him down, and Jekyll's need to cover it up. This is man vs. society.

As the changes continue, Dr. Jekyll becomes weaker, overcome by illness. This is an external conflict, man vs. nature. The ability of the doctor to become someone else suggests yet another external conflict: man vs. the supernatural—because this is not a normal occurrence, and "supernatural" describes anything that is beyond what is natural.

The last conflict is internal: Jekyll has to decide what he must do to stop Hyde, and ultimately, he knows he must change for one last time into Mr. Hyde and then end his life. This is man vs. self.

There are many examples of conflict within the story. Although the circumstances are unusual, the conflicts existing between Dr. Jekyll and his alter-ego are very real and significant.